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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 2025

Date / Time Speaker Title Location
1 October 2025
17:15-18:45 		Prof. Dr. Ivan Kryven
Utrecht University
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Seminar on Stochastic Processes

Title A connection between Burgers’ equation, coagulation processes, and branching
Speaker, Affiliation Prof. Dr. Ivan Kryven, Utrecht University
Date, Time 1 October 2025, 17:15-18:45
Location HG G 43
Abstract We establish a direct correspondence between discrete‐time branching processes and a family of nonlinear evolutionary PDEs generalizing the inviscid Burgers equation. Starting from a simple nonlinear PDE, we show its stochastic analogue is a single‐type branching process with Poisson offspring, closely related to the Erdos-Renyi random graph. By relaxing the PDE’s constraints, this framework naturally extends to multitype branching processes that admit an interpretation as higher‐order coagulation with a multiplicative kernel. Our convergence analysis relies on a new large‐deviation result for the size distribution of finite progenies. Beyond providing an interesting link between PDEs and branching, the representation yields explicit bounds—and in some cases exact expressions—for the blow up time in these nonlinear PDEs.
A connection between Burgers’ equation, coagulation processes, and branchingread_more
HG G 43
8 October 2025
17:15-18:45 		Dr. Martin Minchev
University Zurich
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Seminar on Stochastic Processes

Title Bernstein-gamma functions and exponential functionals of Lévy processes
Speaker, Affiliation Dr. Martin Minchev, University Zurich
Date, Time 8 October 2025, 17:15-18:45
Location HG G 43
Abstract Bernstein-gamma (BG) functions, introduced by Patie and Savov (and also considered in earlier works by Berg, Bertoin, Hirsch, Yor, and others), solve a gamma-type recurrence with a Bernstein function in place of the identity. Their relevance for studying exponential functionals of Lévy processes stems from the fact that the Mellin transform of an EF factors through BG functions. This representation lets us extract asymptotics via Mellin inversion, Tauberian arguments, and links to Wiener-Hopf factors, and, in some cases, it yields weak limits for suitably scaled EF laws. We will sketch some concrete arguments and discuss how these ideas could extend to Markov additive processes through a matrix- or operator-valued analogue of BG functions, noting new obstacles. Joint work with Mladen Savov.
Bernstein-gamma functions and exponential functionals of Lévy processesread_more
HG G 43
22 October 2025
17:15-18:45 		Prof. Dr. Maksim Zhukovskii
University of Sheffield
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Seminar on Stochastic Processes

Title Sharp thresholds for spanning regular subgraphs
Speaker, Affiliation Prof. Dr. Maksim Zhukovskii, University of Sheffield
Date, Time 22 October 2025, 17:15-18:45
Location HG G 43
Abstract A graph property is called increasing if it is closed under addition of edges. For an increasing property, the probability of its occurrence in the binomial random graph G(n,p) transitions rapidly (in asymptotics) from 0 to 1 as p crosses the so-called probability threshold. Since the original paper of Erdős and Rényi the task of determining the asymptotic behaviour of threshold probabilities for increasing properties has been a central topic in probabilistic combinatorics. While the asymptotic order of the probability threshold has been determined for many natural increasing graph properties, a general solution remains unknown, and determining the exact asymptotics is even more challenging. In the talk I will provide an answer to the latter question for a class of increasing properties generated by d-regular graphs. This family of d-regular graphs contains asymptotically almost all d-regular graphs and, in particular, it contains the square of a cycle. This resolves a conjecture of Kahn, Narayanan, and Park, regarding the asymptotics of the threshold for the appearance of the square of a Hamilton cycle.
Sharp thresholds for spanning regular subgraphsread_more
HG G 43
29 October 2025
17:15-18:45 		Prof. Dr. Gaultier Lambert
KTH Royal Institute of Technology
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Seminar on Stochastic Processes

Title Multiplicative chaos for the characteristic polynomial of the circular β-ensemble
Speaker, Affiliation Prof. Dr. Gaultier Lambert, KTH Royal Institute of Technology
Date, Time 29 October 2025, 17:15-18:45
Location HG G 43
Abstract The circular β-ensemble (CβE) is a classical model in random matrix theory which generalizes the eigenvalue process of Haar- distributed unitary random matrix. It can be interpreted as a system of two-dimensional point charges at equilibrium on the unit circle. The goal of this talk is to explain how to describe the asymptotics properties of the CβE characteristic polynomial using the theory of orthogonal polynomials on the unit circle (OPUC). I will show that renormalized powers of the characteristic polynomial converge to multiplicative chaos measures. If time permits, I will explain the connection with the eigenvalue counting function, eigenvalue rigidity and previous results on the CβE spectral measure and the Fyodorov- Bouchaud conjecture. This is joint work with Joseph Najnudel (University of Bristol).
Multiplicative chaos for the characteristic polynomial of the circular β-ensembleread_more
HG G 43
5 November 2025
17:15-18:45 		Dr. Philip Easo
ETH ITS
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Seminar on Stochastic Processes

Title Cutsets and percolation
Speaker, Affiliation Dr. Philip Easo, ETH ITS
Date, Time 5 November 2025, 17:15-18:45
Location HG G 43
Abstract The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G has “not too many small cutsets”. Severo, Tassion, and I have recently proved the converse. Our argument is inspired by an idea from computer science and fits on one page. Our new approach also resolves a conjecture of Babson of Benjamini from 1999 and provides a much simpler proof of the celebrated result of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin that percolation on any transitive graph with superlinear growth undergoes a non-trivial phase transition.
Cutsets and percolationread_more
HG G 43
12 November 2025
17:15-18:45 		Dr. Catherine Cawley Wolfram
ETH Zurich, Switzerland
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Seminar on Stochastic Processes

Title Epstein curves and holography of the Schwarzian action
Speaker, Affiliation Dr. Catherine Cawley Wolfram, ETH Zurich, Switzerland
Date, Time 12 November 2025, 17:15-18:45
Location HG G 43
Abstract The circle can be seen as the boundary at infinity of the hyperbolic plane. We give a 1-to-2 dimensional holographic interpretation of the Schwarzian action, by showing that the Schwarzian action (which is a function of a diffeomorphism of the circle) is equal to the hyperbolic area enclosed by an "Epstein curve" in the disk. A dimension higher, the Epstein construction was used to relate the Loewner energy (a function of a Jordan curve related to SLE and Brownian loop measures) to renormalized volume in hyperbolic 3-space. In this talk I will explain how to construct the Epstein curve, how the bi-local observables of Schwarzian field theory can be interpreted as a renormalized hyperbolic length using the same Epstein construction, and (time permitting) discuss a bit what we know so far about the relationship between the Schwarzian action and the Loewner energy. This is based on joint work with Franco Vargas Pallete and Yilin Wang.
Epstein curves and holography of the Schwarzian actionread_more
HG G 43
19 November 2025
17:15-18:45 		Dr. Max Xu
Courant Institute NYU
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Seminar on Stochastic Processes

Title Primes Make Random Walk Chaotic
Speaker, Affiliation Dr. Max Xu, Courant Institute NYU
Date, Time 19 November 2025, 17:15-18:45
Location HG G 43
Abstract In recent years, probability theory has made a big impact on making progress on many long-standing problems in number theory, and many exciting new probabilistic problems have naturally emerged with strong arithmetic motivations. In this talk, I will tell you part of the story of their interactions. Many of the connections can be summarized as a random walk problem, but with influences from primes. You may find the story interesting if any of the following keywords catch your attention: the Ballot problem, Log-correlated fields, Gaussian multiplicative chaos, Fydorov-Hiary-Keating conjecture, Polya's conjecture, random polynomials, distribution of primes.
Primes Make Random Walk Chaoticread_more
HG G 43
26 November 2025
17:15-18:45 		Prof. Dr. Christophe Sabot
Université Claude Bernard Lyon 1
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Seminar on Stochastic Processes

Title A random polymer approach to the weak disorder phase of the Vertex Reinforced Jump Process
Speaker, Affiliation Prof. Dr. Christophe Sabot, Université Claude Bernard Lyon 1
Date, Time 26 November 2025, 17:15-18:45
Location HG G 43
Abstract The Vertex Reinforced Jump Process (VRJP) is a continuous-time process closely related to the linearly edge reinforced random walk. The recurrence/transience of the VRJP can be caracterized by the asymptotic behavior of a positive martingale : the VRJP is recurrent when the limit is null and transient when it is positive. Besides, the L^p integrability of that martingale is related to the diffusive behavior of the VRJP. A large part of the talk will be devoted to recall some key properties of the VRJP and to explain how that martingale appears and how it can be interpreted as the partition function of a non-directed polymer in a very specific 1-dependent potential. At the end, we will show new results about the L^p integrability of the martingale, using the polymer interpretation and taking inspiration from some works of Junk on directed polymers, Based on a joint work with Q. Berger, A. Legrand and R. Poudevigne-Auboiron.
A random polymer approach to the weak disorder phase of the Vertex Reinforced Jump Processread_more
HG G 43
3 December 2025
17:15-18:45 		Dr. Joffrey Mathien
Aix-Marseille Université (AMU)
Details

Seminar on Stochastic Processes

Title Cutoff for geodesic path and Brownian motion on hyperbolic manifolds
Speaker, Affiliation Dr. Joffrey Mathien, Aix-Marseille Université (AMU)
Date, Time 3 December 2025, 17:15-18:45
Location HG G 43
Abstract For an ergodic dynamical system, the cutoff describes an abrupt transition to equilibrium. Historically introduced in seminal work by Diaconis, Shahshahani and Aldous for card shuffling and other random walks on finite groups, there are now numerous examples of Markov chains and Markov processes where the cutoff has been established. Most of the current examples are on finite spaces. In this talk, we study cutoff for classical processes -- namely Brownian motion and geodesic paths -- on compact hyperbolic manifolds, and we develop a spectral strategy introduced by Lubetzky and Peres in 2016 for Ramanujan graphs and further developed in different geometric contexts. In particular, we extend results obtained by Golubev and Kamber in 2019 to any dimension and still are able to obtain cutoff under weaker hypothesis. Joint work with C. Bordenave
Cutoff for geodesic path and Brownian motion on hyperbolic manifoldsread_more
HG G 43
10 December 2025
17:15-18:45 		Dr. Francesco Pedrotti
ETH Zurich, Switzerland
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Seminar on Stochastic Processes

Title Cutoff for the proximal sampler via transport inequalities
Speaker, Affiliation Dr. Francesco Pedrotti, ETH Zurich, Switzerland
Date, Time 10 December 2025, 17:15-18:45
Location HG G 43
Abstract The cutoff phenomenon is a sharp transition in the convergence of high-dimensional Markov chains to equilibrium: the total variation distance remains close to 1 for a long time and then rapidly decreases to almost 0 over a much shorter time window. It was initially discovered in the context of card shuffling by Diaconis and Shahshahani, and since then observed in a variety of different models. In spite of its ubiquity, it is still largely unexplained, and most proofs are model-specific. In this talk, we discuss a high-level approach to establishing cutoff based on transport inequalities, and we illustrate it on a popular algorithm known as the proximal sampler, when the target measure on Rd is log-concave. Based on joint work with Justin Salez.
Cutoff for the proximal sampler via transport inequalitiesread_more
HG G 43
17 December 2025
17:15-18:45 		Prof. Dr. Jacopo Borga
MIT
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Seminar on Stochastic Processes

Title Directed distance on bipolar-oriented triangulations: A path toward the directed Liouville quantum gravity metrics
Speaker, Affiliation Prof. Dr. Jacopo Borga, MIT
Date, Time 17 December 2025, 17:15-18:45
Location HG G 43
Abstract Last and first passage percolation in two dimensions are classical discrete models of random directed planar Euclidean metrics in the KPZ universality class. Their scaling limit is described by the directed landscape of Dauvergne-Ortmann-Virág. Random planar maps are classical discrete models of random undirected planar fractal metrics in the LQG universality class. Their scaling limit is described by the (undirected) LQG metric of Ding-Dubédat-Dunlap-Falconet and Gwynne-Miller. We present recent progress on the study of longest and shortest directed paths in the following natural model of directed random planar maps: the uniform infinite bipolar-oriented triangulation (UIBOT), which is the local limit of uniform bipolar-oriented triangulations around a typical edge and is expected to be in the LQG universality class with γ=√4/3. We first explain the analogies between this model and last and first passage percolation. Then, we construct the Busemann function, which measures directed distance to infinity along a natural interface of the UIBOT. We show that, in the case of longest (resp. shortest) directed paths, this Busemann function converges in the scaling limit to a 2/3-stable Lévy process (resp. a 4/3-stable Lévy process). These results imply that in a typical subset of the UIBOT with n edges, longest directed path lengths are of order n^{3/4} and shortest directed path lengths are of order n^{3/8}. We conclude the talk by explaining why these results fit into a program to construct the (longest and shortest) directed LQG metrics, two distinct two-parameter families of random fractal directed metrics which generalize the LQG metric and which could conceivably converge to the directed landscape upon taking an appropriate limit. Based on joint work with E. Gwynne.
Directed distance on bipolar-oriented triangulations: A path toward the directed Liouville quantum gravity metricsread_more
HG G 43

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