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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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Spring Semester 2026

Date / Time Speaker Title Location
25 February 2026
17:15-18:45 		Dr. Sahar Rabin Diskin
ETH Zurich, Switzerland
Details

Seminar on Stochastic Processes

Title Mixing time and diameter of the percolated hypercube
Speaker, Affiliation Dr. Sahar Rabin Diskin, ETH Zurich, Switzerland
Date, Time 25 February 2026, 17:15-18:45
Location Y27 H12
Abstract We study bond percolation on the d-dimensional hypercube Q^d with edge retention probability p=c/d. It is well known that when c>1 is fixed, a unique giant component emerges. In this regime, we resolve conjectures of Bollobás, Kohayakawa, and Łuczak (1994) and of Benjamini and Mossel (2003), showing that the typical diameter of the giant component is Θ(d), and that the mixing time of the lazy random walk on it is Θ(d^2). In the talk, we will introduce the notion of mixing time and its connection to expansion properties of subsets of the giant. We will then discuss some of the key obstacles in obtaining this result, and in particular why classical sprinkling techniques are insufficient for this problem. Finally, we will explain how our new approach - based on analysing the effect of small perturbations and establishing stability under thinning - overcomes these obstacles. This method also yields tight large-deviation estimates for the size of the giant. Based on joint work with Michael Anastos, Lyuben Lichev, and Maksim Zhukovskii.
Mixing time and diameter of the percolated hypercuberead_more
Y27 H12
4 March 2026
17:15-18:45 		Prof. Dr. Yueyun Hu
Université Sorbonne Paris Nord
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Seminar on Stochastic Processes

Title Average-weight percolation on the complete graph
Speaker, Affiliation Prof. Dr. Yueyun Hu, Université Sorbonne Paris Nord
Date, Time 4 March 2026, 17:15-18:45
Location Y27 H12
Abstract This talk is based on a joint work with Elie Aidékon (Shanghai). Attach to each edge of the complete graph on $n$ vertices, i.i.d. exponential random variables with mean $n$. Aldous (1998) proved that the longest path with average weight below $p$ undergoes a phase transition at $p=\frac{1}{e}$: it is $o(n)$ when $p<\frac{1}{e}$ and of order $n$ if $p>\frac1e$. Later, Ding (2013) revealed a finer phase transition around $\frac{1}{e}$: there exist $c'>c>0$ such that the length of the longest path is of order $\ln^3 n$ if $ p \le \frac{1}{e}+\frac{c}{\ln^2 n}$ and is polynomial if $p\ge \frac{1}{e}+\frac{c'}{\ln^2 n}$. We identify the location of this phase transition and obtain sharp asymptotics of the length near criticality. The proof uses an exploration mechanism mimicking a branching random walk with selection introduced by Brunet and Derrida (1999).
Average-weight percolation on the complete graphread_more
Y27 H12
11 March 2026
17:15-18:45 		Prof. Dr. Loïc Béthancourt
Université Sorbonne Paris Nord
Details

Seminar on Stochastic Processes

Title Fractional diffusion limit in convex domain and reflected isotropic stable processes
Speaker, Affiliation Prof. Dr. Loïc Béthancourt, Université Sorbonne Paris Nord
Date, Time 11 March 2026, 17:15-18:45
Location Y27 H12
Abstract In this talk, I will present some recent results obtained with Nicolas Fournier. We are interested in a simple model describing the (random) motion of a particle in a gaz, namely the kinetic scattering equation. When the particle lives in $\mathbb{R}^d$, and when the equilibrium (for the velocities) is heavy-tailed, it is easy to see that the position process, correctly rescaled, converges weakly to an $\alpha$-stable process. We are interested in the case where the particle is confined into a convex smooth domain, by a certain reflection mechanism that I will describe. We show that, according to the boundary condition, two different types of reflected stable process may arise at the limit. After introducing the model and the results, I will mostly explain how we construct the limiting processes by piecing together their excursions inside the domain. If time permits, I will say a few words about the convergence.
Fractional diffusion limit in convex domain and reflected isotropic stable processesread_more
Y27 H12
18 March 2026
17:15-18:45 		Dr. Benjamin Bonnefont
Université de Genève
Details

Seminar on Stochastic Processes

Title Fourier dimension of imaginary Gaussian multiplicative chaos
Speaker, Affiliation Dr. Benjamin Bonnefont, Université de Genève
Date, Time 18 March 2026, 17:15-18:45
Location Y27 H12
Abstract Recent works have established sharp Fourier decay for subcritical real Gaussian multiplicative chaos (GMC) on the circle, and in this talk I will discuss the corresponding harmonic picture for imaginary GMC. Gaussian multiplicative chaos is obtained by exponentiating log-correlated Gaussian fields; on the unit circle, one may take the trace of the two-dimensional Gaussian free field with covariance $\log 1/|e^{i\theta}-e^{i\theta'}|$. For purely imaginary parameters $\gamma=i\beta$ with $\beta\in(0,1)$, the resulting object $M_{i\beta}$ exists as a complex-valued random distribution and enjoys strong integrability properties. The Fourier dimension captures the decay of the Fourier coefficients $c_n$ of a distribution. It is defined as the supremum of $s\in(0,1)$ such that $|c_n|^2 = O(|n|^{-s})$. We prove that the Fourier dimension of $M_{i\beta}$ is almost surely $1-\beta^2$ and establish a joint CLT for the rescaled coefficients. The proof uses the method of moments specific to the imaginary regime. The moments of $c_n$ (and mixed moments of nearby modes) are rewritten as Coulomb-gas integrals on the circle, and then analysed via the Selberg inner product and Jack polynomial expansions, which convert the moment integrals into positive partition sums amenable to sharp asymptotic analysis. Joint work with Hermanni Rajamäki and Vincent Vargas.
Fourier dimension of imaginary Gaussian multiplicative chaosread_more
Y27 H12
1 April 2026
17:15-18:45 		Dr. Isao Sauzedde
ENS de Lyon
Details

Seminar on Stochastic Processes

Title Title T.B.A.
Speaker, Affiliation Dr. Isao Sauzedde, ENS de Lyon
Date, Time 1 April 2026, 17:15-18:45
Location Y27 H12
Title T.B.A.
Y27 H12
22 April 2026
17:15-18:45 		Dr. Yuhao Xue
IHES
Details

Seminar on Stochastic Processes

Title Title T.B.A.
Speaker, Affiliation Dr. Yuhao Xue, IHES
Date, Time 22 April 2026, 17:15-18:45
Location Y27 H12
Title T.B.A.
Y27 H12

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