Seminar on Stochastic Processes

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Autumn Semester 2023

Date / Time

Speaker

Title

Location

27 September 2023
17:15-18:45

Prof. Dr. Grégory Miermont
ENS Lyon

Event Details

Seminar on Stochastic Processes

Title	Compact Brownian surfaces
Speaker, Affiliation	Prof. Dr. Grégory Miermont, ENS Lyon
Date, Time	27 September 2023, 17:15-18:45
Location	Y27 H12
Abstract	We describe the compact scaling limits of uniformly random quadrangulations with boundaries on a surface of arbitrary fixed genus. These limits, called Brownian surfaces, are homeomorphic to the surface of the given genus with or without boundaries depending on the scaling regime of the boundary perimeters of the quadrangulation. They are constructed by appropriate gluings of pieces derived from Brownian geometrical objects (the Brownian plane and half-plane). In this talk, I will review their definition and discuss possible alternative constructions. This is based on joint work with Jérémie Bettinelli.

Compact Brownian surfacesread_more

Y27 H12

4 October 2023
17:15-18:45

Prof. Dr. Igor Kortchemski
ETH Zürich

Event Details

Seminar on Stochastic Processes

Title	Global freezing
Speaker, Affiliation	Prof. Dr. Igor Kortchemski, ETH Zürich
Date, Time	4 October 2023, 17:15-18:45
Location	Y27 H12

Global freezing

Y27 H12

11 October 2023
17:15-18:45

Prof. Dr. Aleksandar Mijatovic
University of Warwick

Event Details

Seminar on Stochastic Processes

Title	Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability
Speaker, Affiliation	Prof. Dr. Aleksandar Mijatovic, University of Warwick
Date, Time	11 October 2023, 17:15-18:45
Location	Y27 H12
Abstract	In this talk we quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the domain that separate stability, null recurrence and transience. In the stable case we prove existence and uniqueness of the invariant distribution and establish the polynomial rate of decay of its tail. We also establish matching polynomial upper and lower bounds on the rate of convergence to stationarity in total variation. All exponents are explicit in the model parameters that determine the asymptotics of the growth rate of the domain, the interior covariance, and the reflection vector field. Proofs are probabilistic, and use upper and lower tail bounds for additive functionals up to return times to compact sets, for which we develop novel sub/supermartingale criteria, applicable to general continuous semimartingales. Time permitting, I will discuss the main ideas behind the proofs in the talk. This is joint work with Miha Bresar (Warwick) and Andrew Wade (Durham).

Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stabilityread_more

Y27 H12

25 October 2023
17:15-18:45

Prof. Dr. Nathanael Berestycki
University of Vienna

Event Details

Seminar on Stochastic Processes

Title	Weyl law in Liouville quantum gravity
Speaker, Affiliation	Prof. Dr. Nathanael Berestycki, University of Vienna
Date, Time	25 October 2023, 17:15-18:45
Location	Y27 H12
Abstract	Can you hear the shape of Liouville quantum gravity (LQG)? We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the n-th eigenvalue grows linearly with n, with the proportionality constant given by the Liouville measure of the domain and a certain deterministic constant which is computed explicitly and is, surprisingly, strictly greater than its Riemannian counterpart. After explaining this result and its context, as well as some related estimates pertaining to the small-time behaviour of the heat kernel, I hope to also present a number of conjectures on the spectral geometry of LQG. These relate both to the behaviour of eigenfunctions (suggesting intriguing connections with so-called "quantum chaos") and to that of eigenvalues, for which we conjecture a connection to random matrix statistics. This is joint work with Mo-Dick Wong (Durham).

Weyl law in Liouville quantum gravityread_more

Y27 H12

1 November 2023
17:15-18:45

Prof. Dr. Jean Bertoin
Universität Zürich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	Working group step-reinforced random walk: general presentation
Speaker, Affiliation	Prof. Dr. Jean Bertoin, Universität Zürich, Switzerland
Date, Time	1 November 2023, 17:15-18:45
Location	Y27 H12

Working group step-reinforced random walk: general presentation

Y27 H12

8 November 2023
17:15-18:45

Prof. Dr. Erich Baur
Berner Fachhochschule, Technik und Informatik

Event Details

Seminar on Stochastic Processes

Title	Random walks with reinforced memory
Speaker, Affiliation	Prof. Dr. Erich Baur, Berner Fachhochschule, Technik und Informatik
Date, Time	8 November 2023, 17:15-18:45
Location	Y27 H12
Abstract	We discuss various models of random walks with a reinforced memory originating from the well-known Elephant Random Walk. We concentrate on models with a linear reinforcement mechanism, where the weight of a step is increased by an additive factor if the step is remembered, making it therefore likelier to repeat the step again and again in the future. We will also discuss the counterbalanced versions of these walks.

Random walks with reinforced memoryread_more

Y27 H12

15 November 2023
17:15-18:45

Dr. Alejandro Rosales Ortiz
Universität Zürich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	Working group step-reinforced random walks: Joint invariance principles
Speaker, Affiliation	Dr. Alejandro Rosales Ortiz, Universität Zürich, Switzerland
Date, Time	15 November 2023, 17:15-18:45
Location	Y27 H12

Working group step-reinforced random walks: Joint invariance principles

Y27 H12

22 November 2023
17:15-18:45

Prof. Dr. Daniel Ueltschi
University of Warwick

Event Details

Seminar on Stochastic Processes

Title	The Kac-Ward solution of the 2D Ising model
Speaker, Affiliation	Prof. Dr. Daniel Ueltschi, University of Warwick
Date, Time	22 November 2023, 17:15-18:45
Location	Y27 H12
Abstract	Onsager proposed a closed-form expression of the free energy of the Ising model in 1944. The method of Kac and Ward is particularly elegant and it has recently be made rigorous by Lis and Aizenman-Warzel. I will show how to extend it to the triangular lattice, with coupling constants of arbitrary signs. This is ongoing work with Georgios Athanasopoulos.

The Kac-Ward solution of the 2D Ising modelread_more

Y27 H12

6 December 2023
17:15-18:45

Zheng Fang
Universität Zürich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	Working group step-reinforced random walks: Recurrence of 2D Elephant Random Walk
Speaker, Affiliation	Zheng Fang, Universität Zürich, Switzerland
Date, Time	6 December 2023, 17:15-18:45
Location	Y27 H12

Working group step-reinforced random walks: Recurrence of 2D Elephant Random Walk

Y27 H12

13 December 2023
17:15-18:45

Daniela Portillo del Valle
Universität Zürich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	Working group step-reinforced random walks: On the distribution of the limiting velocity
Speaker, Affiliation	Daniela Portillo del Valle, Universität Zürich, Switzerland
Date, Time	13 December 2023, 17:15-18:45
Location	Y27 H12

Working group step-reinforced random walks: On the distribution of the limiting velocity

Y27 H12

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