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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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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 Y27H12
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
Y27H12
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 Y27H12
Global freezing
Y27H12
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 Y27H12
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
Y27H12
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 Y27H12
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
Y27H12
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 Y27H12
Working group step-reinforced random walk: general presentation
Y27H12
8 November 2023
17:15-18:45		 Prof. Dr. Erich Baur
Berner Fachhochschule, Technik und Informatik
Event Details

Seminar on Stochastic Processes

Title Working group step-reinforced random walks: 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 Y27H12
Working group step-reinforced random walks: random walks with reinforced memory
Y27H12
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 Y27H12
Working group step-reinforced random walks: Joint invariance principles
Y27H12
22 November 2023
17:15-18:45		 Prof. Dr. Daniel Ueltschi
University of Warwick
Event Details

Seminar on Stochastic Processes

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Daniel Ueltschi,University of Warwick
Date, Time 22 November 2023, 17:15-18:45
Location Y27H12
Title T.B.A.
Y27H12
2023年11月29日
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 2023年11月29日, 17:15-18:45
Location Y27H12
Working group step-reinforced random walks: On the distribution of the limiting velocity
Y27H12
6 December 2023
17:15-18:45		 Zheng Fang
Universität Zürich, Switzerland
Event Details

Seminar on Stochastic Processes

Title 工作组step-reinforced随机漫步:Recurrence of 2D Elephant Random Walk
Speaker, Affiliation Zheng Fang,Universität Zürich, Switzerland
Date, Time 6 December 2023, 17:15-18:45
Location Y27H12
工作组step-reinforced随机漫步:Recurrence of 2D Elephant Random Walk
Y27H12

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