Date/Time : 08 Dec 2021 09:00
Venue : via Zoom
Speaker : Konstantin Matetski, Columbia University

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https://nus-sg.zoom.us/j/89132660362?pwd=SHB5bkRwVU9UUDRKVUd0UzY0Vk02QT09

Meeting ID: 891 3266 0362
Passcode: 880312

The KPZ universality class includes random growing interfaces, which, after rescaling, are conjectured to converge to the KPZ fixed point. The latter is a Markov process, which has been characterized through the exact solution of TASEP, a particular model in the class. The KPZ equation plays a special role and is conjectured to be the only model connecting the Edwards-Wilkinson (Gaussian) and the KPZ fixed points. In the talk, I will introduce the KPZ fixed point and review recent work on the KPZ universality done by myself and my collaborators.

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Date/Time : 01 Dec 2021 16:00
Venue : via Zoom
Speaker : Pierre-Francois Rodriguez, Imperial College, London

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https://nus-sg.zoom.us/j/85694125031?pwd=eGJuMWk5SXRCS2hWc1JITXpRWmdRUT09

Meeting ID: 856 9412 5031
Passcode: 918464

Abstract: I will report on recent progress regarding the near-critical behavior of certain statistical physics models in dimension 3. Our results deal with the critical scaling exponents associated to the second-order phase transition for two percolation problems involving the Gaussian free field in 3D. In one case, they determine a unique “fixed point” corresponding to the transition, which is proved to obey one of several scaling relations. Such laws are classically conjectured to hold by physicists on the grounds of a corresponding scaling ansatz.

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Date/Time : 24 Nov 2021 09:00
Venue : via Zoom
Speaker : Yair Shenfeld, MIT

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https://nus-sg.zoom.us/j/87967891890?pwd=R1k4L2FLUGZKVURjd0ZiU0h5L013dz09

Meeting ID: 879 6789 1890
Passcode: 176920

Abstract: What does a ball and a half space have in common? The former is the unique shape which minimizes surface area among all shapes of equal Euclidean volume, while the latter solves the analogous optimization problem for Gaussian volume. These shapes are examples of extremal structures and they play a prominent role in geometric and
probabilistic phenomena: from the shape of water droplets to concentration of measure.

Once we go deeper into the world of extremal structures, we find that they seem hopelessly complex, while permeating mathematics, ranging from probability to combinations to algebraic geometry. In fact, the
characterization of some of these structures is only conjectural, while for others, not even conjectures exist. I will talk about how we resolve several of these conjectures using stochastic, analytic, and geometric tools.

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Date/Time : 17 Jan 2020 14:00
Venue : S16 #05-98
Speaker : Xinyi Li , Peiking University

Date/Time:17 Jan 2020 14:00 Venue: S16 #05-98 Speaker: Xinyi Li, Peiking University Recent Progress on Loop-erased Random Walk In this mini-course, we will give a brief review on the model of Loop-erased Random Walk (LERW) and its relationship with other models from statistical physics, and discuss some of the recent progress on this model, especially in three dimensions. Add to calendar: 

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Date/Time : 16 Jan 2020 14:00
Venue : S16 #05-98
Speaker : Xinyi Li , Peiking University

Date/Time:16 Jan 2020 14:00 Venue: S16 #05-98 Speaker: Xinyi Li, Peiking University Recent Progress on Loop-erased Random Walk In this mini-course, we will give a brief review on the model of Loop-erased Random Walk (LERW) and its relationship with other models from statistical physics, and discuss some of the recent progress on this model, especially in three dimensions. Add to calendar: 

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Date/Time : 15 Jan 2020 14:00
Venue : S16 #05-98
Speaker : Xinyyi Li , Peiking University

Date/Time:15 Jan 2020 14:00 Venue: S16 #05-98 Speaker: Xinyyi Li, Peiking University Recent Progress on Loop-erased Random Walk In this mini-course, we will give a brief review on the model of Loop-erased Random Walk (LERW) and its relationship with other models from statistical physics, and discuss some of the recent progress on this model, especially in three dimensions. Add to calendar: 

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Date/Time : 20 Feb 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Alexander Drewitz , U. Cologne

Date/Time:20 Feb 2019 14:00 Venue: S17 #04-06 SR1 Speaker: Alexander Drewitz, U. Cologne Geometry of Gaussian free field sign clusters and random interlacements We consider two fundamental percolation models with long-range correlations: Level set percolation for the Gaussian free field (GFF) and percolation of the vacant set of random interlacements. Both models have been the subject of intensive research during the last decades. In this talk we focus on structural properties of the level set percolation of the GFF. In particular, we establish the non-triviality of a phase in which two infinite sign clusters dominate, and their complement only has small connected components. While the respective results are new for $\Z^d$ as the underlying graph, we also cover more intricate geometries such as transient graphs with subdiffusive random walk behavior. As a consequence, we answer an open problem on the non-triviality of the phase transition of the vacant set of Random Interlacements on such geometries. This talk is based on joint works with A. Prévost (Universität zu Köln) and P.-F. Rodriguez (IHES). Add to calendar: 

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Date/Time : 05 Feb 2019 14:00
Venue : S17 #05-11 SR5
Speaker : Yuki Tokushige , Kyoto University

Date/Time:05 Feb 2020 14:00 Venue: S17 #05-11 SR5 Speaker: Yuki Tokushige, Kyoto University Jump processes on the Gromov boundary induced by RWs on a hyperbolic group In this talk, we will discuss a class of jump processes on the Gromov boundary induced by random walks on a hyperbolic group. In particular, we will show that there is a kind of canonical potential theoretic structure on the Gromov boundary, which is associated to a certain conformal structure of the boundary. We will start the talk with discussions about basic facts on Dirichlet forms and hyperbolic groups. This talk is based on a joint work with Pierre Mathieu. (Aix-Marseille University) Add to calendar: 

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Date/Time : 27 Jul 2018 15:00
Venue : S16 #05-96
Speaker : Asaf Hajiyev, Azerbaijan National Academy of Sciences

Date/Time:27 Jul 2018 15:00 Venue: S16 #05-96 Speaker: Asaf Hajiyev, Azerbaijan National Academy of Sciences Some Paradoxical Phenomena in Theory of Probability and The mathematical models of moving particles, describing a behavior of traffic, communication, queuing and other systems are considered. Motion of particles depends on a distance between them. It is provided that in stationary regime each separately considered particle makes the binomial random walk. This fact allows to calculate some characteristics of traffic systems and predict a traffic jam. In the capacity of an efficiency index in these systems, an average waiting time of particle in the fixed point is taken. A control function is introduced, which means delay of some particles during motion. The class of systems for which introducing of delays can reduce an efficiency index is described. The optimal function minimizing an efficiency index is found. Numerical examples demonstrating results are given. Add to calendar: 

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