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

Join Zoom Meeting
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.

Add to calendar :

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: 

Add to calendar :

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: 

Add to calendar :

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: 

Add to calendar :

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: 

Add to calendar :

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: 

Add to calendar :

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: 

Add to calendar :

Date/Time : 27 Jun 2018 15:30
Venue : S17 #04-04 SR3
Speaker : Johnson, Liu Qiang , University of Macau

Date/Time:27 Jun 2018 15:30 Venue: S17 #04-04 SR3 Speaker: Johnson, Liu Qiang, University of Macau Inference of Spot Volatility in the presence of Infinite Variation Jumps Empirical evidences witness that the jumps appear to be very frequent in the financial markets. In this talk, we propose a kernel estimator for the spot volatility of an Ito semi-martingale at a given time point by using the high frequency data, under the circumstance that the jumps contained in the underlying driven process could be of infinite variation. The estimator is based on the representation of the characteristic function of Levy processes. The consistency of the proposed estimator is established under some mild assumptions. By assuming that the jump part of the underlying process behaves like a symmetric stable Levy process around 0, we establish the asymptotic normality of the proposed estimator. In particular, with a specific kernel function, the estimator is variance efficient. We conduct Monte Carlo simulation studies to assess our theoretical results. We also extend our theories to the estimation of spot covariation quantities between two Ito semi-martingales. Our estimators are applied to some real high frequency financial data sets for empirical analysis. Add to calendar: 

Add to calendar :

Date/Time : 23 May 2018 10:30
Venue : S17 #04-06 SR1
Speaker : Claudia Klüppelberg , Technical University of Munich

Date/Time:23 May 2018 10:30 Venue: S17 #04-06 SR1 Speaker: Claudia Klüppelberg, Technical University of Munich Max-linear models on graphs Graphical models are a popular tool to analyse and visualise dependence properties between random variables; see e.g. Lauritzen (1996). Each node in the graph represents a random variable, and the absence of an edge between two nodes indicates conditional independence between the corresponding random variables. We introduce a new recursive structural equation model, where all random variables can be written as a max-linear function of their parents and independent noise variables. In particular, we define directed graphical models, where edge orientations come along with an intuitive causal interpretation and present conditional independence properties of the model. Furthermore, we use algebraic methods to characterise all max-linear models, which are generated by a structural equation model and detail the relation between the coefficients of the structural equation model (the edge weights of the graph) and the max-linear coefficients. Finally, we extend finite-dimensional max-linear models to models on infinite graphs, and investigate their relations to classical percolation theory, more precisely to nearest neighbour Bernoulli bond percolation. The talk is based on joint work with Nadine Gissibl, Steffen Lauritzen, Moritz Otto, and Ercan Sönmetz. Add to calendar: 

Add to calendar :