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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Frühjahrssemester 2023

Datum / Zeit Referent:in Titel Ort
1. März 2023
17:15-18:45 		Prof. Dr. Francesco Caravenna
Department of Mathematics and Applications, University of Milano-Bicocca
Details

Seminar on Stochastic Processes

Titel The critical 2d Stochastic Heat Flow
Referent:in, Affiliation Prof. Dr. Francesco Caravenna, Department of Mathematics and Applications, University of Milano-Bicocca
Datum, Zeit 1. März 2023, 17:15-18:45
Ort Y27 H12
Abstract We consider the 2-dimensional Stochastic Heat Equation (SHE), which falls outside the scope of existing solution theories for singular stochastic PDEs. When we regularise the SHE by discretising space-time, the solution can be identified with the partition function of a statistical mechanics model, the so-called directed polymer in random environment. We prove that as the discretisation is removed and the noise strength is rescaled in a critical way, the solution converges to a unique continuum limit: a universal process of random measures on R^2, which we call the critical 2d Stochastic Heat Flow. We investigate its features, showing in particular that it cannot be the exponential of a generalised Gaussian field. Based on joint work with R. Sun and N. Zygouras.
The critical 2d Stochastic Heat Flowread_more
Y27 H12
8. März 2023
17:15-18:45 		Dr. Vincent Vargas
Ecole normale supérieure de Paris
Details

Seminar on Stochastic Processes

Titel Title T.B.A.
Referent:in, Affiliation Dr. Vincent Vargas, Ecole normale supérieure de Paris
Datum, Zeit 8. März 2023, 17:15-18:45
Ort Y27 H12
Title T.B.A. (ABGESAGT)
Y27 H12
15. März 2023
17:15-18:45 		Dr. Barbara Dembin
ETH Zurich
Details

Seminar on Stochastic Processes

Titel Upper tail large deviations for chemical distance in supercritical percolation
Referent:in, Affiliation Dr. Barbara Dembin, ETH Zurich
Datum, Zeit 15. März 2023, 17:15-18:45
Ort Y27 H12
Abstract We consider supercritical bond percolation on Z^d and study the chemical distance, i.e., the graph distance on the infinite cluster. It is well-known that there exists a deterministic constant μ(x) such that the chemical distance D(0,nx) between two connected points 0 and nx grows like nμ(x). We prove the existence of the rate function for the upper tail large deviation event {D(0,nx)>nμ(x)(1+ϵ),0↔nx} for d>=3. Joint work with Shuta Nakajima.
Upper tail large deviations for chemical distance in supercritical percolationread_more
Y27 H12
22. März 2023
17:15-18:45 		Dr. François Bienvenu
Inst. für Theoretische Studien, ETH
Details

Seminar on Stochastic Processes

Titel A branching process with coalescence to model random phylogenetic networks
Referent:in, Affiliation Dr. François Bienvenu, Inst. für Theoretische Studien, ETH
Datum, Zeit 22. März 2023, 17:15-18:45
Ort Y27 H12
A branching process with coalescence to model random phylogenetic networks
Y27 H12
5. April 2023
17:15-18:45 		Prof. Dr. Bastien Mallein
Université Sorbonne Paris Nord
Details

Seminar on Stochastic Processes

Titel Extremal process of multidimensional branching Brownian motion
Referent:in, Affiliation Prof. Dr. Bastien Mallein, Université Sorbonne Paris Nord
Datum, Zeit 5. April 2023, 17:15-18:45
Ort Y27 H12
Abstract The branching Brownian motion is a particle system in which each particle evolves independently of one another. Each particle moves according to a Brownian motion in dimension d, and splits into two daughter particles after an independent exponential time of parameter 1. The daughter particles then start from their positions independent copies of the same process. We take interest in the long time asymptotic behaviour of the particles reaching farthest away from the origin. We show that these particles can be found at a distance of order $\sqrt{2} t + \frac{d-4}{2\sqrt{2}} \log t$ from the origin of the process, and that they can be grouped into a Poisson point process of families of close relatives, spreading in directions sampled according to the random measure $Z(\mathrm{d} \theta)$ that plays the role of an analogue of the derivative martingale of the branching Brownian motion.
Extremal process of multidimensional branching Brownian motionread_more
Y27 H12
19. April 2023
17:15-18:45 		Prof. Dr. Elliot Paquette
Department of Mathematics and Statistics, McGill University
Details

Seminar on Stochastic Processes

Titel The random matrix Fyodorov-Hiary-Keating conjecture
Referent:in, Affiliation Prof. Dr. Elliot Paquette, Department of Mathematics and Statistics, McGill University
Datum, Zeit 19. April 2023, 17:15-18:45
Ort Y27 H12
Abstract The Fyodorov-Hiary-Keating conjecture has two parts, one in random matrix theory and one about the Riemann zeta function. In the random matrix part, it gives the precise distributional limit for the maximum of a characteristic polynomial of a Haar Unitary matrix. Using the replica method and a physically motivated `freezing’ ansatz, they derived one of the most precise log-correlated field predictions todate, and they did it for a process which was not even Gaussian. While existing work shows that Haar Unitary matrices had many log correlated field connections, techniques for showing convergence of the maximum typically rely on either the Gaussianity of the underlying process or precise branching structures built into the problem; the characteristic polynomial has neither. We will describe the problem and the current state of the art, in which we (the speaker and Ofer Zeitouni) show the convergence in law of the maximum of a Circular-beta ensemble random matrix to a convolution of a gumbel and the total mass of a (non-Gaussian) critical multiplicative chaos.
The random matrix Fyodorov-Hiary-Keating conjectureread_more
Y27 H12
10. Mai 2023
17:15-18:45 		Prof. Dr. Cyril Marzouk
École polytechnique
Details

Seminar on Stochastic Processes

Titel Scaling limits of random maps with prescribed face degrees
Referent:in, Affiliation Prof. Dr. Cyril Marzouk, École polytechnique
Datum, Zeit 10. Mai 2023, 17:15-18:45
Ort Y27 H12
Abstract Random planar maps are toy models in random geometry that allow to easily define discrete random surfaces. One hope that when letting the number of faces tend to infinity and their size to zero at the correct speed, one can get a continuum random surface, in the same way Brownian motion arises from large random walks. A decade ago, after a series of works by different authors, the convergence of random quadrangulations and a few other models to the so-called Brownian map was finally obtained simultaneously by Le Gall and Miermont. In this talk we will discuss the more general model of maps sampled uniformly at random given their face degrees and will discuss the convergence depending on these degrees.
Scaling limits of random maps with prescribed face degreesread_more
Y27 H12

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