Departement Mathematik

Seminar on stochastic processes

Members of the probability group are involved in co-organizing remote specialized seminars that take place on Tuesdays and Thursdays:

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Herbstsemester 2023

Datum / Zeit Referent:in Titel Ort
27. September 2023
17:15-18:45 		Prof. Dr. Grégory Miermont
ENS Lyon
Details

Seminar on Stochastic Processes

Titel Compact Brownian surfaces
Referent:in, Affiliation Prof. Dr. Grégory Miermont, ENS Lyon
Datum, Zeit 27. September 2023, 17:15-18:45
Ort 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. Oktober 2023
17:15-18:45 		Prof. Dr. Igor Kortchemski
ETH Zürich
Details

Seminar on Stochastic Processes

Titel Global freezing
Referent:in, Affiliation Prof. Dr. Igor Kortchemski, ETH Zürich
Datum, Zeit 4. Oktober 2023, 17:15-18:45
Ort Y27 H12
Global freezing
Y27 H12
11. Oktober 2023
17:15-18:45 		Prof. Dr. Aleksandar Mijatovic
University of Warwick
Details

Seminar on Stochastic Processes

Titel Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability
Referent:in, Affiliation Prof. Dr. Aleksandar Mijatovic, University of Warwick
Datum, Zeit 11. Oktober 2023, 17:15-18:45
Ort 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. Oktober 2023
17:15-18:45 		Prof. Dr. Nathanael Berestycki
University of Vienna
Details

Seminar on Stochastic Processes

Titel Weyl law in Liouville quantum gravity
Referent:in, Affiliation Prof. Dr. Nathanael Berestycki, University of Vienna
Datum, Zeit 25. Oktober 2023, 17:15-18:45
Ort 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
Details

Seminar on Stochastic Processes

Titel Working group step-reinforced random walk: general presentation
Referent:in, Affiliation Prof. Dr. Jean Bertoin, Universität Zürich, Switzerland
Datum, Zeit 1. November 2023, 17:15-18:45
Ort 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
Details

Seminar on Stochastic Processes

Titel Random walks with reinforced memory
Referent:in, Affiliation Prof. Dr. Erich Baur, Berner Fachhochschule, Technik und Informatik
Datum, Zeit 8. November 2023, 17:15-18:45
Ort 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
Details

Seminar on Stochastic Processes

Titel Working group step-reinforced random walks: Joint invariance principles
Referent:in, Affiliation Dr. Alejandro Rosales Ortiz, Universität Zürich, Switzerland
Datum, Zeit 15. November 2023, 17:15-18:45
Ort 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
Details

Seminar on Stochastic Processes

Titel The Kac-Ward solution of the 2D Ising model
Referent:in, Affiliation Prof. Dr. Daniel Ueltschi, University of Warwick
Datum, Zeit 22. November 2023, 17:15-18:45
Ort 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. Dezember 2023
17:15-18:45 		Zheng Fang
Universität Zürich, Switzerland
Details

Seminar on Stochastic Processes

Titel Working group step-reinforced random walks: Recurrence of 2D Elephant Random Walk
Referent:in, Affiliation Zheng Fang, Universität Zürich, Switzerland
Datum, Zeit 6. Dezember 2023, 17:15-18:45
Ort Y27 H12
Working group step-reinforced random walks: Recurrence of 2D Elephant Random Walk
Y27 H12
13. Dezember 2023
17:15-18:45 		Daniela Portillo del Valle
Universität Zürich, Switzerland
Details

Seminar on Stochastic Processes

Titel Working group step-reinforced random walks: On the distribution of the limiting velocity
Referent:in, Affiliation Daniela Portillo del Valle, Universität Zürich, Switzerland
Datum, Zeit 13. Dezember 2023, 17:15-18:45
Ort Y27 H12
Working group step-reinforced random walks: On the distribution of the limiting velocity
Y27 H12

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