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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 2024

Date / Time Speaker Title Location
16 October 2024
17:15-18:45 		Dr. Alejandro Rosales Ortiz
Universität Zürich, Switzerland
Details

Seminar on Stochastic Processes

Title Excursion theory for Brownian motion indexed by the Brownian tree
Speaker, Affiliation Dr. Alejandro Rosales Ortiz, Universität Zürich, Switzerland
Date, Time 16 October 2024, 17:15-18:45
Location HG G 43
Abstract We begin by introducing the notion of Brownian motion indexed by the Brownian tree. We will then present the main aspects of a theory, developed in two recent works with Armand Riera, that describes the evolution of this tree-indexed process between visits to 0. The theory applies to fairly general continuous Markov processes indexed by Lévy trees. Despite the radically different setting, we will see that our results share strong similarities with the celebrated Itô excursion theory for linear Brownian motion. If time permits, we will also discuss some applications to Brownian geometry.
Excursion theory for Brownian motion indexed by the Brownian treeread_more
HG G 43
23 October 2024
17:15-18:45 		Prof. Dr. Jean Bertoin
Universität Zürich, Switzerland
Details

Seminar on Stochastic Processes

Title Graduate Workshop Reinforcement
Speaker, Affiliation Prof. Dr. Jean Bertoin, Universität Zürich, Switzerland
Date, Time 23 October 2024, 17:15-18:45
Location Y27 H26
Graduate Workshop Reinforcement
Y27 H26
30 October 2024
17:15-18:45 		Prof. Dr. Jean Bertoin
Universität Zürich, Switzerland
Details

Seminar on Stochastic Processes

Title Graduate Workshop Reinforcement
Speaker, Affiliation Prof. Dr. Jean Bertoin, Universität Zürich, Switzerland
Date, Time 30 October 2024, 17:15-18:45
Location Y27 H26
Graduate Workshop Reinforcement
Y27 H26
6 November 2024
17:15-18:45 		Daniela Portillo del Valle
Universität Zürich, Switzerland
Details

Seminar on Stochastic Processes

Title Graduate Workshop Reinforcement
Speaker, Affiliation Daniela Portillo del Valle, Universität Zürich, Switzerland
Date, Time 6 November 2024, 17:15-18:45
Location Y27 H26
Graduate Workshop Reinforcement
Y27 H26
13 November 2024
17:15-18:45 		Prof. Dr. Ana Djurdjevac
Freie Universität Berlin
Details

Seminar on Stochastic Processes

Title Quantitative approximation of the Dean-Kawasaki equation with interactions
Speaker, Affiliation Prof. Dr. Ana Djurdjevac, Freie Universität Berlin
Date, Time 13 November 2024, 17:15-18:45
Location HG G 43
Abstract Interacting particle systems provide flexible and powerful models that are useful in many application areas such as sociology (agents), molecular dynamics (proteins) etc. However, particle systems with large numbers of particles are very complex and difficult to handle, both analytically and computationally. Therefore, a common strategy is to derive effective equations that describe the time evolution of the empirical particle density. A prototypical example that we will consider is the formal identification of a finite system of particles with the singular Dean-Kawasaki equation. Our aim is to introduce a well-behaved nonlinear SPDE that approximates the Dean-Kawasaki equation for a particle system with mean-field interaction both in the drift and the noise term. We want to study the well-posedness of these nonlinear SPDE models and to control the weak error of the SPDE approximation with respect to the particle system using the technique of transport equations on the space of probability measures. This is the joint work with H. Kremp, N. Perkowski and J. Xiaohao.
Quantitative approximation of the Dean-Kawasaki equation with interactionsread_more
HG G 43
20 November 2024
17:15-18:45 		Dr. Antoine Jego
EPFL, Lausanne (From Nov 2024: Ceremade, Paris Dauphine)
Details

Seminar on Stochastic Processes

Title Crossing exponent of the Brownian loop soup
Speaker, Affiliation Dr. Antoine Jego, EPFL, Lausanne (From Nov 2024: Ceremade, Paris Dauphine)
Date, Time 20 November 2024, 17:15-18:45
Location HG G 43
Abstract We study the clusters of loops in a Brownian loop soup in some bounded two-dimensional domain with subcritical intensity θ ∈ (0, 1/2]. We obtain an exact expression for the asymptotic probability of the existence of a cluster crossing a given annulus of radii r and rs as r → 0 (s > 1 fixed). Relying on this result, we then show that the probability for a macroscopic cluster to hit a given disc of radius r decays like | log r|−1+θ+o(1) as r → 0. Finally, we characterise the polar sets of clusters, i.e. sets that are not hit by the closure of any cluster, in terms of logα-capacity.
Crossing exponent of the Brownian loop soupread_more
HG G 43
27 November 2024
17:15-18:45 		Dr. Gabriel Berzunza
University of Liverpool
Details

Seminar on Stochastic Processes

Title Fringe trees for random trees with given vertex degrees
Speaker, Affiliation Dr. Gabriel Berzunza, University of Liverpool
Date, Time 27 November 2024, 17:15-18:45
Location HG G 43
Abstract In this talk, we consider fringe trees of random plane trees with given vertex statistics (i.e., a given number of vertices of each degree). The main results are laws of large numbers and central limit theorems for the number of fringe trees of a given type. The key tool for our proofs is an extension to the multivariate setting of a theorem by Gao and Wormald (2004), which provides a way to show asymptotic normality by analyzing the behaviour of sufficiently high factorial moments. Our results also apply to random simply generated trees (or conditioned Galton–Watson trees) by conditioning on their degree statistic. Joint work with Cecilia Holmgren and Svante Janson (Uppsala University)
Fringe trees for random trees with given vertex degreesread_more
HG G 43
4 December 2024
17:15-18:45 		Prof. Dr. Sergei Kuksin
Universite Paris-Diderot (Paris 7)
Details

Seminar on Stochastic Processes

Title On rigorous 1d versions of the laws of Kolmogorov’s theory of turbulence
Speaker, Affiliation Prof. Dr. Sergei Kuksin, Universite Paris-Diderot (Paris 7)
Date, Time 4 December 2024, 17:15-18:45
Location HG G 43
Abstract In his celebrated theory of turbulence, created in 1941 and known as the K41 theory, A.N.Kolmogorov considered the velocity u(t,x) of a turbulent flow of fluid. Assuming that the Reynolds number of the flow is large, he studied the increments u(t,x+r)-u(t,x) of u and heuristically examined their statistical properties, summarised in a number of law of the K41 theory. I will talk about fictitious 1d fluid, described by the stochastic Burgers equation, consider increments of its velocity field and will rigorously derive for them analogies of the corresponding laws from Kolmogorov's theory, strikingly close to these laws.
On rigorous 1d versions of the laws of Kolmogorov’s theory of turbulenceread_more
HG G 43
11 December 2024
17:15-18:45 		Zheng Fang
Universität Zürich, Switzerland
Details

Seminar on Stochastic Processes

Title Graduate Workshop Reinforcement
Speaker, Affiliation Zheng Fang, Universität Zürich, Switzerland
Date, Time 11 December 2024, 17:15-18:45
Location Y27 H26
Graduate Workshop Reinforcement
Y27 H26
18 December 2024
17:15-18:45 		Dr. Dirk Zeindler
Lancaster University
Details

Seminar on Stochastic Processes

Title Partitions into semi-primes
Speaker, Affiliation Dr. Dirk Zeindler, Lancaster University
Date, Time 18 December 2024, 17:15-18:45
Location HG G 43
Abstract In this talk we will look at some recent developments about integer partitions, including coloured partitions, semi-prime partitions and r-prime partitions. We will give asymptotic formulae for the number of these partitions. We will also look at some interesting elements of the proof of these formulae, without going into too much technical detail. In particular, we have a look at strange and pseudo-differentiable functions.
Partitions into semi-primesread_more
HG G 43

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