Noticias en español
Diameter and mixing time of the giant component in the percolated hypercube.
Resumen: The d-dimensional binary hypercube is the graph whose vertices represent the binary vectors of length d and two vertices are adjacent if they differ in a single coordinate. The percolated hypercube (where every edge is retained independently with probability p) is a classic model in random graph theory. In this talk, we are going to survey some of the history of the model and discuss recent estimates of the mixing time of the lazy simple random walk and the diameter of the giant component in a supercritical percolated hypercube. Based on a joint work with Michael Anastos, Sahar...
Read MoreDrift parameter estimation for a fractional interacting particle system.
Resumen: We consider a system of interacting particles with Lipschitz continuous drift functions, driven by additive fractional Brownian motions with H in [1/2, 1). For this system, we address the drift parameter estimation problem from continuous observations over a fixed time interval, assuming that the drift depends linearly on an unknown parameter vector. We propose estimators inspired by the least squares approach, demonstrate their consistency and asymptotic normality as the number of particles tends to infinity, and present a numerical study illustrating our findings. The proofs rely...
Read MoreThe rightmost particle of the inherited sterility contact process.
Resumen: The contact process with inherited sterility provides a probabilistic framework for studying population control strategies inspired by the Sterile Insect Technique. In this model, an infected particle can create a fertile infected particle (with probability p) or a sterile infected particle (with probability 1-p) which will behave like an “environment” blocking the propagation of the infection. The main challenge is that this model is not attractive (since an increase of fertile individuals potentially causes that of sterile ones). Sonia Velasco previously proved that this process...
Read MoreOn fraudulent stochastic algorithms.
Resumen: We introduce and analyse the almost sure convergence of a stochastic algorithm for the global minimisation of smooth functions. This diffusion process is called fraudulent because it requires the knowledge of minimal value of the function. Nevertheless, its investigation is not without interest, since in particular it appears as the limit behaviour of non-fraudulent and time-inhomogeneous swarm mean-field algorithms for global optimisation or in stochastic gradient descent algorithms in over-parametrised deep learning applications. The talk is based on collaborations with Benaïm,...
Read MoreQuenched limits for sub-ballistic random walks in random conductances: high and low dimensions.
Resumen: Consider a random walk amongst elliptic conductances with a deterministic directional bias. For all dimensions larger or equal than 2, Fribergh proved that the walk is ballistic if and only if the mean of a conductance is finite. In the infinite mean case, under proper regularity conditions, Fribergh and Kious showed the convergence of the rescaled process towards Fractional Kinetics, in the annealed setting. I will explain how to obtain a quenched limit by exploiting a celebrated idea of Bolthausen and Sznitman. I will highlight the difference between the high dimensional case (d...
Read MoreRandom burning of the Euclidean lattice.
Resumen: The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point to set on fire, and the fire propagates constantly at unit speed along the edges of the graph. In joint work with Alice Contat, following Mitsche, Prałat and Roshanbin, we consider two natural random burning procedures in the discrete Euclidean torus $\mathbb{T}_n^d$, in which the points that we set on fire at each step are random variables. Our main result deals with the case where at each step, the...
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