{"plugins":["moment","interaction","dayGrid","timeGrid","list","rrule"],"timeZone":"Europe\/Paris","defaultView":"listYear","defaultDate":"2023-05-31","header":{"left":"prev,next today","center":"title","right":"dayGridMonth,timeGridWeek,timeGridDay,listYear"},"eventTimeFormat":"[]","firstDay":1,"minTime":"08:00:00","maxTime":"19:00:00","weekends":false,"locale":"en","events":[{"title":"Systems of weakly self-avoiding polygons","id":"0-0","eid":"4896","url":"\/fr\/node\/4896","des":"Wed, 05\/31\/2023 - 09:15<\/time>\n - Wed, 05\/31\/2023 - 10:15<\/time>\n\n

Systems of weakly self-avoiding polygons<\/a> <\/h2>\nLorenzo Taggi\n
Title: Systems of weakly self-avoiding polygons
\nAbstract: We consider systems of weakly self-avoiding loops interacting by mutual repulsion. The model depends on a parameter which rewards the total loop length. This model is not only mathematically interesting on its own, but it is also a description of other relevant statistical mechanics models, such as the Spin O(N) model and the double dimer model, and it is related to the Bose gas. The main question is understanding the typical size of the loops in the limit of large boxes and the phase transition phenomenon. This mini-course will provide an overview and present some of the main mathematical techniques, such as reflection positivity.<\/p>","editable":false,"start":"2023-05-31T09:15:00","end":"2023-05-31T10:15:00","backgroundColor":"#3a87ad"},{"title":"Break","id":"1-0","eid":"4900","url":"\/fr\/node\/4900","des":"Wed, 05\/31\/2023 - 10:30<\/time>\n - Wed, 05\/31\/2023 - 10:45<\/time>\n\n
Break<\/a> <\/h2>\nBreak\n","editable":false,"start":"2023-05-31T10:30:00","end":"2023-05-31T10:45:00","backgroundColor":"#3a87ad"},{"title":"Derrida Retaux Model","id":"2-0","eid":"4899","url":"\/fr\/node\/4899","des":"Wed, 05\/31\/2023 - 11:00<\/time>\n - Wed, 05\/31\/2023 - 12:00<\/time>\n\n
Derrida Retaux Model<\/a> <\/h2>\nYueyun Hu\n
Yueyun Hu
\nTitle: Derrida Retaux Model<\/p>\n\n
Abstract: In order to study the depinning transition in presence of strong disorder, Derrida and Retaux (J. Stat. Phys. (2014)) introduced a discrete-time max-type recursive model. It is believed that for a large class of recursive models, including the Derrida and Retaux model, there are highly non-trivial universalities at and near the critical regimes. In this mini-course, we will review some recent results and open questions on this model, as well as a continuous time model for which we study a solvable case and con rme the corresponding conjectures.
\nThe mini course is based on joint works with Xinxing Chen, Victor Dagard, Bernard Derrida, Mikhail Lifshits, and Zhan Shi on the discrete-time model and with Bastien Mallein and Michel Pain on the continuous time model.<\/p>","editable":false,"start":"2023-05-31T11:00:00","end":"2023-05-31T12:00:00","backgroundColor":"#3a87ad"},{"title":"Break","id":"3-0","eid":"4900","url":"\/fr\/node\/4900","des":"Wed, 05\/31\/2023 - 12:15<\/time>\n - Wed, 05\/31\/2023 - 13:30<\/time>\n\n
Break<\/a> <\/h2>\nBreak\n","editable":false,"start":"2023-05-31T12:15:00","end":"2023-05-31T13:30:00","backgroundColor":"#3a87ad"},{"title":"Collapse transition for a three-dimensional partially directed polymer.","id":"4-0","eid":"4901","url":"\/fr\/node\/4901","des":"Wed, 05\/31\/2023 - 13:45<\/time>\n - Wed, 05\/31\/2023 - 14:30<\/time>\n\n
Collapse transition for a three-dimensional partially directed polymer.<\/a> <\/h2>\nFrank den Hollander\n
In this talk we look at a three-dimensional version of a twodimensional polymer in a poor resolvent that was analysed in detail by P. Carmona, G.B. Nguyen and N. Petrelis. Polymers are partially directed self-avoiding walks. Each pair of non-consecutive nearestneighbour monomers contributes a negative energy to the interaction Hamiltonian. The interaction strengths are 0 for monomers in di erent hyperplanes and 0 for monomers in the same hyperplane. We derive a variational formula for the excess free energy per monomer ~ f( ; ), and prove that there is a collapse transition between an extended phase E = f ; 0: ~ f( ; ) > 0g and a collapsed phase C = f ; 0: ~ f( ; ) = 0g. We identify the shape of the critical
\ncurve separating the two phases, and obtain information on the typical behaviour of the polymer in the two phases. Work in progress with N. Petrelis (Nantes).<\/p>","editable":false,"start":"2023-05-31T13:45:00","end":"2023-05-31T14:30:00","backgroundColor":"#3a87ad"},{"title":"Speed of biased random walk on dynamical percolation","id":"5-0","eid":"4902","url":"\/fr\/node\/4902","des":"Wed, 05\/31\/2023 - 14:30<\/time>\n - Wed, 05\/31\/2023 - 15:15<\/time>\n\n
Speed of biased random walk on dynamical percolation<\/a> <\/h2>\nPerla Sousi \n
We study the speed of a biased random walk on dynamical percolation on Zd as a function of the bias. While in dimension one, the speed is easily seen to be monotone increasing, we show that in higher dimensions this fails and some new phenomena occur. This is joint work with Sebastian Andres, Nina Gantert and Dominik Schmid.<\/p>","editable":false,"start":"2023-05-31T14:30:00","end":"2023-05-31T15:15:00","backgroundColor":"#3a87ad"},{"title":"Weakly self-avoiding walk in a random potential (PART 1)","id":"6-0","eid":"4903","url":"\/fr\/node\/4903","des":"Wed, 05\/31\/2023 - 15:45<\/time>\n - Wed, 05\/31\/2023 - 16:30<\/time>\n\n
Weakly self-avoiding walk in a random potential (PART 1)<\/a> <\/h2>\nWillem van Zuijlen\n
We investigate a model of simple-random walk paths in a random environment that has two competing features: an attractive one towards the highest values of a random potential, and a selfrepellent one in the spirit of the well-known weakly self-avoiding random walk. We tune the strength of the second effect such that they both contribute on the same scale as the time variable tends to infinity. In this talk I will discuss our results on the identification of (1) the logarithmic asymptotics of the partition function, and (2) of the path behaviour that gives the overwhelming contribution to the partition function. This is joint work with Wolfgang Konig, Nicolas Petrelis and Renato Soares dos Santos.<\/p>","editable":false,"start":"2023-05-31T15:45:00","end":"2023-05-31T16:30:00","backgroundColor":"#3a87ad"},{"title":"Weakly self-avoiding walk in a random potential (PART 2)","id":"7-0","eid":"4904","url":"\/fr\/node\/4904","des":"Wed, 05\/31\/2023 - 16:30<\/time>\n - Wed, 05\/31\/2023 - 17:15<\/time>\n\n
Weakly self-avoiding walk in a random potential (PART 2)<\/a> <\/h2>\nRenato Soares Dos Stantos\n
This is a follow-up talk on part 1 in which we discuss the ideas behind the proof, that rely on a point measure representation and Gamma convergence of our energy and entropy functionals.<\/p>","editable":false,"start":"2023-05-31T16:30:00","end":"2023-05-31T17:15:00","backgroundColor":"#3a87ad"},{"title":"Derrida Retaux Model","id":"8-0","eid":"4899","url":"\/fr\/node\/4899","des":"Thu, 06\/01\/2023 - 09:15<\/time>\n - Thu, 06\/01\/2023 - 10:15<\/time>\n\n
Derrida Retaux Model<\/a> <\/h2>\nYueyun Hu\n
Yueyun Hu
\nTitle: Derrida Retaux Model<\/p>\n\n
Abstract: In order to study the depinning transition in presence of strong disorder, Derrida and Retaux (J. Stat. Phys. (2014)) introduced a discrete-time max-type recursive model. It is believed that for a large class of recursive models, including the Derrida and Retaux model, there are highly non-trivial universalities at and near the critical regimes. In this mini-course, we will review some recent results and open questions on this model, as well as a continuous time model for which we study a solvable case and con rme the corresponding conjectures.
\nThe mini course is based on joint works with Xinxing Chen, Victor Dagard, Bernard Derrida, Mikhail Lifshits, and Zhan Shi on the discrete-time model and with Bastien Mallein and Michel Pain on the continuous time model.<\/p>","editable":false,"start":"2023-06-01T09:15:00","end":"2023-06-01T10:15:00","backgroundColor":"#3a87ad"},{"title":"Break","id":"9-0","eid":"4900","url":"\/fr\/node\/4900","des":"Thu, 06\/01\/2023 - 10:30<\/time>\n - Thu, 06\/01\/2023 - 10:45<\/time>\n\n
Break<\/a> <\/h2>\nBreak\n","editable":false,"start":"2023-06-01T10:30:00","end":"2023-06-01T10:45:00","backgroundColor":"#3a87ad"},{"title":"Systems of weakly self-avoiding polygons","id":"10-0","eid":"4896","url":"\/fr\/node\/4896","des":"Thu, 06\/01\/2023 - 11:00<\/time>\n - Thu, 06\/01\/2023 - 12:00<\/time>\n\n
Systems of weakly self-avoiding polygons<\/a> <\/h2>\nLorenzo Taggi\n
Title: Systems of weakly self-avoiding polygons
\nAbstract: We consider systems of weakly self-avoiding loops interacting by mutual repulsion. The model depends on a parameter which rewards the total loop length. This model is not only mathematically interesting on its own, but it is also a description of other relevant statistical mechanics models, such as the Spin O(N) model and the double dimer model, and it is related to the Bose gas. The main question is understanding the typical size of the loops in the limit of large boxes and the phase transition phenomenon. This mini-course will provide an overview and present some of the main mathematical techniques, such as reflection positivity.<\/p>","editable":false,"start":"2023-06-01T11:00:00","end":"2023-06-01T12:00:00","backgroundColor":"#3a87ad"},{"title":"Break","id":"11-0","eid":"4900","url":"\/fr\/node\/4900","des":"Thu, 06\/01\/2023 - 12:15<\/time>\n - Thu, 06\/01\/2023 - 13:15<\/time>\n\n
Break<\/a> <\/h2>\nBreak\n","editable":false,"start":"2023-06-01T12:15:00","end":"2023-06-01T13:15:00","backgroundColor":"#3a87ad"},{"title":"The scaling limit for directed polymers in an alpha-stable environment","id":"12-0","eid":"4905","url":"\/fr\/node\/4905","des":"Thu, 06\/01\/2023 - 13:30<\/time>\n - Thu, 06\/01\/2023 - 14:15<\/time>\n\n
The scaling limit for directed polymers in an alpha-stable environment<\/a> <\/h2>\nHubert Lacoin\n
Directed polymers in a random environment is a model of statistical mechanics introduced in the 80s. Given a set if independent, identically random variable n;x indexed by N Zd, and a parameter > 0, it is de ned as the measure on the set of nearest neighbor path of length N, (Sn)N n=0 which to each path gives a weight proportional to QN i=1(1 + n;Sm).
\nThe aim of this talk is to discuss the existence of a continuum scaling limit for this model if the parameter is sent to zero when N tends to in nity. We will rst introduce the topic to the audience by reviewing a result of Alberts, Khanin and Quastel in 2014 which establishes the existence of such a scaling limit in dimension 1 under the assumption that the environment has a nite second moment. Afterwards we will present our main results which:<\/p>\n\n
1. Establishes the existence of another family of continuum model based on -stable noise rather than Gaussian white noise,
\n2. Show that this continuum model can be obtained as the scaling limit of the discrete polymer when the random environment is heavy tailed.<\/p>","editable":false,"start":"2023-06-01T13:30:00","end":"2023-06-01T14:15:00","backgroundColor":"#3a87ad"},{"title":"Renewal Theory, Disordered Systems, and Stochastic PDEs","id":"13-0","eid":"4906","url":"\/fr\/node\/4906","des":"Thu, 06\/01\/2023 - 14:15<\/time>\n - Thu, 06\/01\/2023 - 15:00<\/time>\n\n
Renewal Theory, Disordered Systems, and Stochastic PDEs<\/a> <\/h2>\nFrancesco Caravenna\n
We present a renewal theorem for random walks with \"ultra heavy tails\", which converge after rescaling to an explicit Levy process called the Dickman subordinator. Besides its own interest, such a renewal theorem is the key to a ne understanding of a challenging model in statistical mechanics, the directed polymer in random environment in the critical space dimension d=2, and of a singular stochastic PDE, the multiplicative Stochastic Heat Equation. We discuss the relations between these seemingly unrelated models, which
\nled to important recent progress. (Based on joint work with R. Sun and N. Zygouras)<\/p>","editable":false,"start":"2023-06-01T14:15:00","end":"2023-06-01T15:00:00","backgroundColor":"#3a87ad"},{"title":"Generalized Hawkes processes","id":"14-0","eid":"4907","url":"\/fr\/node\/4907","des":"Thu, 06\/01\/2023 - 15:30<\/time>\n - Thu, 06\/01\/2023 - 16:15<\/time>\n\n
Generalized Hawkes processes<\/a> <\/h2>\nLaure Coutin\n
Hawkes processes, initially introduced to model the occurrence of earthquakes and their after-shocks, are currently used in a growing number of elds such as neuroscience, nance and insurance. These point processes model the successive occurrences of events and their influence on the probability of future occurrences. We briefly present Hawkes processes. Following previous investigations by Ustunel about the invertibility of some transformations on the Wiener space, we nd some entropic conditions under which a random change of time is invertible on the Poisson space. As a conse- quence, we provide a construction of (genrealized) Hawkes processes as a random time change of Poisson\u00a0 process. We also establish a new variational representation of the entropy.<\/p>","editable":false,"start":"2023-06-01T15:30:00","end":"2023-06-01T16:15:00","backgroundColor":"#3a87ad"},{"title":"Non-intersecting Brownian bridges, KPZ, and random matrices","id":"15-0","eid":"4908","url":"\/fr\/node\/4908","des":"Thu, 06\/01\/2023 - 16:15<\/time>\n - Thu, 06\/01\/2023 - 17:00<\/time>\n\n
Non-intersecting Brownian bridges, KPZ, and random matrices<\/a> <\/h2>\nGia-Bao Nguyen\n
I will discuss a system of N non-intersecting Brownian bridges on the time interval [-1; 1] where N - m paths start and end at the origin and the m top paths go between arbitrary positions. This system is known to generate several universal determinantal processes as scaling limits. I will focus on the distribution of the limiting maximal height for this system, which provides a deformation of the Tracy-Widom GOE distribution in random matrix theory. I will present a Fredholm determinant formula for this distribution function.
\nI also discuss the connection with KPZ fluctuations, as well as some results on relations with Painleve II and other PDEs. This is based on joint work with Daniel Remenik and Karl Liechty.<\/p>","editable":false,"start":"2023-06-01T16:15:00","end":"2023-06-01T17:00:00","backgroundColor":"#3a87ad"},{"title":"Systems of weakly self-avoiding polygons","id":"16-0","eid":"4896","url":"\/fr\/node\/4896","des":"Fri, 06\/02\/2023 - 09:15<\/time>\n - Fri, 06\/02\/2023 - 10:15<\/time>\n\n
Systems of weakly self-avoiding polygons<\/a> <\/h2>\nLorenzo Taggi\n
Title: Systems of weakly self-avoiding polygons
\nAbstract: We consider systems of weakly self-avoiding loops interacting by mutual repulsion. The model depends on a parameter which rewards the total loop length. This model is not only mathematically interesting on its own, but it is also a description of other relevant statistical mechanics models, such as the Spin O(N) model and the double dimer model, and it is related to the Bose gas. The main question is understanding the typical size of the loops in the limit of large boxes and the phase transition phenomenon. This mini-course will provide an overview and present some of the main mathematical techniques, such as reflection positivity.<\/p>","editable":false,"start":"2023-06-02T09:15:00","end":"2023-06-02T10:15:00","backgroundColor":"#3a87ad"},{"title":"Break","id":"17-0","eid":"4900","url":"\/fr\/node\/4900","des":"Fri, 06\/02\/2023 - 10:30<\/time>\n - Fri, 06\/02\/2023 - 10:45<\/time>\n\n
Break<\/a> <\/h2>\nBreak\n","editable":false,"start":"2023-06-02T10:30:00","end":"2023-06-02T10:45:00","backgroundColor":"#3a87ad"},{"title":"Derrida Retaux Model","id":"18-0","eid":"4899","url":"\/fr\/node\/4899","des":"Fri, 06\/02\/2023 - 11:00<\/time>\n - Fri, 06\/02\/2023 - 12:00<\/time>\n\n
Derrida Retaux Model<\/a> <\/h2>\nYueyun Hu\n
Yueyun Hu
\nTitle: Derrida Retaux Model<\/p>\n\n
Abstract: In order to study the depinning transition in presence of strong disorder, Derrida and Retaux (J. Stat. Phys. (2014)) introduced a discrete-time max-type recursive model. It is believed that for a large class of recursive models, including the Derrida and Retaux model, there are highly non-trivial universalities at and near the critical regimes. In this mini-course, we will review some recent results and open questions on this model, as well as a continuous time model for which we study a solvable case and con rme the corresponding conjectures.
\nThe mini course is based on joint works with Xinxing Chen, Victor Dagard, Bernard Derrida, Mikhail Lifshits, and Zhan Shi on the discrete-time model and with Bastien Mallein and Michel Pain on the continuous time model.<\/p>","editable":false,"start":"2023-06-02T11:00:00","end":"2023-06-02T12:00:00","backgroundColor":"#3a87ad"},{"title":"Break","id":"19-0","eid":"4900","url":"\/fr\/node\/4900","des":"Fri, 06\/02\/2023 - 12:15<\/time>\n - Fri, 06\/02\/2023 - 13:15<\/time>\n\n
Break<\/a> <\/h2>\nBreak\n","editable":false,"start":"2023-06-02T12:15:00","end":"2023-06-02T13:15:00","backgroundColor":"#3a87ad"},{"title":"Disorder relevance in one dimensional random \feld Ising chains","id":"20-0","eid":"4909","url":"\/fr\/node\/4909","des":"Fri, 06\/02\/2023 - 13:30<\/time>\n - Fri, 06\/02\/2023 - 14:15<\/time>\n\n
Disorder relevance in one dimensional random \feld Ising chains<\/a> <\/h2>\nGiambattista Giacomin\n
I will present recent progress in the analysis of the top Lyapunov exponent for the Ising transfer matrix products and analogous results in the continuum limit of this model. These results aim at understanding of the e ect of disorder in the one dimensional nearer neighbor Ising model with deterministic pair interaction J and disordered external magnetic eld, in the limit J > infinite. The emphasis will be on the role of disorder.<\/p>\n<\/div>","editable":false,"start":"2023-06-02T13:30:00","end":"2023-06-02T14:15:00","backgroundColor":"#3a87ad"},{"title":"The prudent self-avoiding walk in dimension six and higher","id":"21-0","eid":"4910","url":"\/fr\/node\/4910","des":"Fri, 06\/02\/2023 - 14:15<\/time>\n - Fri, 06\/02\/2023 - 15:00<\/time>\n\n
The prudent self-avoiding walk in dimension six and higher<\/a> <\/h2>\nNiccollo Torri\n
The prudent self-avoiding random walk (P-SAW) is a family of self-avoiding walks in which the walk cannot take any step in the direction of a previously visited site, which is an in nite-range repellence condition. The prudent walk was originally introduced as a class of self-avoiding walks which are simple to modelize. In the last 20 years this walk has attracted the attention of the combinatorics and probability communities and, until recently, only the dimension d = 2 was completely described. In this talk we discuss the behaviour of the uniform P-SAW in high dimension. Our main result states that the P-SAW converges to Brownian motion under di usive scaling if the dimension is large enough. The same result is true for weakly prudent walk in dimension d > 5, which is greater than the critical dimension of the classical self-avoiding walk. Our approach is based on the\u00a0 lace expansion. In a first part of the talk we discuss the interest to study this family of self-avoiding random walks, while in a second part we present the main tools used for the analysis of the walk.<\/p>","editable":false,"start":"2023-06-02T14:15:00","end":"2023-06-02T15:00:00","backgroundColor":"#3a87ad"},{"title":"Adsorption transition at the surface of a self-avoiding, collapsed polymer","id":"22-0","eid":"4911","url":"\/fr\/node\/4911","des":"Fri, 06\/02\/2023 - 15:30<\/time>\n - Fri, 06\/02\/2023 - 16:15<\/time>\n\n
Adsorption transition at the surface of a self-avoiding, collapsed polymer<\/a> <\/h2>\nAlexandre Legrand\n
The adsorption phase transition of a polymer to an attractive hard wall is a well-known phenomenon, and has been studied extensively in the mathematics literature: if the attraction intensity to the wall is larger than some critical value, the polymer gets localized in the vicinity of the wall, otherwise it wanders away. In this talk we additionally consider that the polymer is dipped in a poor solvent, with which it interacts repulsively. If the repulsion intensity is large, the polymer folds over on itself into a compact globule, minimizing its
\ninteractions with the solvent. We prove that in this \"collapsed\" regime, the polymer still undergoes the aforementioned adsorption transition. However, only the outter, bottommost layer of the globule may adhere to the wall: therefore this is not a proper phase transition, and does not appear in the free energy; this phenomenon is called a \"surface transition\", and is proven by deriving sharp asymptotics of the partition function of this model.<\/p>","editable":false,"start":"2023-06-02T15:30:00","end":"2023-06-02T16:15:00","backgroundColor":"#3a87ad"}],"navLinks":true,"editable":false,"eventLimit":5,"eventOverlap":true}