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DTSTART;TZID=Europe/Paris:20260518T000000
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SUMMARY:Recent Progress on Self-Interacting Processes and Non-Reversible Monte Carlo
DESCRIPTION:Toutes les informations de la conférence sur la page de l’évènement \nAnthony Maggs: Large scale dynamics of non-reversible Monte Carlo algorithmsMonte Carlo simulation is a workhorse of the numerical study of physical systems at thermodynamic equilibrium. Non-reversible Monte Carlo algorithms replace the commonly used constraint of detailed balance with global balance. We give examples of situations where this leads to accelerated sampling of physical systems. We argue that the large-scale relaxation of such Event-Chain Monte Carlo methods is linked to the dynamics of the true self-avoiding walk. \nFrancis Lörler: Event Chain Monte Carlo\, self-repellent random walks\, and the stochastic heat equationThe Event Chain Monte Carlo algorithm is an MCMC method for sampling equilibrium configurations of interacting particles. When applied to a harmonic chain of oscillators\, it is closely related to the self-repellent random walk on a discrete circle. We show that these processes are second-order lifts of a discrete stochastic heat equation with additive noise. As a consequence\, we obtain a lower bound on the relaxation times of order n^{3/2}. Moreover\, we show that when the active particle is resampled with an appropriate rate\, then the relaxation time has an upper bound of order n^2. On the same model\, optimally tuned Hamiltonian Monte Carlo achieves a relaxation time of order n^{5/4}\, but due to the gradient evaluations\, its complexity is of order n^{9/4}. This confirms a conjecture of Werner Krauth that on this specific model\, ECMC can outperform HMC. Joint work with Andreas Eberle. \nBrune Massoulié: From the lifted TASEP to true self-avoiding walksThe lifted TASEP is a variant of the totally asymmetric exclusion process where at each time-step\, instead of trying to move forward a uniformly chosen particle\, a marked particle tries to move forward then may pass the marker to another particle. It was introduced by physicists as a toy model for non-reversible event-chain Monte-Carlo algorithms\, which are expected to reach equilibrium faster than reversible dynamics. We will study the behaviour of this system on the integer line by evidencing a connection with true self-avoiding walks\, yielding timescales of the dynamics. This is based on joint work with Clément Erignoux\, Werner Krauth\, François Simenhaus and Cristina Toninelli. \nFrancesco Coghi and Juan Garrahan: Self-interacting processes: from tensor networks to level 2.5 large deviationsIn this combined presentation\, we discuss two aspects of self-interacting processes (stochastic processes whose transition rates depend on empirical observables). First we show\, using a tensor network approach\, a connection to Doob conditioning\, such that Markov processes with constrained occupation measures are optimally realised by self-interacting dynamics. Second\, exploiting a natural separation of timescales\, we formulate the exact large deviation statistics for the joint empirical measure and flux\, thus extending the classical Markov theory to this non-Markovian setting. \nJonathon Peterson: Limit Theorems for self-interacting random walks: a Ray-Knight approachIn this talk I will discuss recent results\, joint with Kosygina\, Mareche\, and Mountford\, which show how one can use “joint Ray-Knight theorems” to prove functional limit laws for certain self-interacting random walks. Recent results of myself and co-authors have used these techniques to prove scaling limits for the “true” self-avoiding random walk and also for polynomially self-repelling random walks. For “true” self-avoiding walks we confirm a conjecture of Toth and Werner that the scaling limit is the “true” self-repelling motion. For polynomially self-repelling walks the scaling limit is a new process (the polynomially self-repelling motion) which has the same marginal distributions as a (1/2\, 1/2)-Brownian motion perturbed at its extrema\, but which has different joint distributions. \nLaure Marêché: Limit behavior for the self-repelling random walk with directed edgesThe self-repelling random walk with directed edges on Z was introduced by Tóth and Vető in 2008. It is a random walk with a memory\, such that the probability to cross a directed edge of Z is smaller if this edge was already crossed a lot in the past. Its definition resembles that of the more studied self-interacting random walks introduced by Tóth in 1994\,1995\,1996\, with directed edges instead of undirected edges. However\, this seemingly minor change yields a sharp difference in the behavior of the walk\, and the self-repelling random walk with directed edges on Z turns out to have very unusual properties\, which we will present in this talk. \nJulien Brémont: The memory of geometry in self-interacting random walks : eccentricity and flip statisticsObserving a particular set of visited sites strongly impacts the future for a self-interacting random walk\, as it conditions the past trajectory in a certain way. In one dimension\, the geometry of the past visited territory is described by the number of visited sites n\, and the eccentricity z\, that is the fraction of positive visited sites. How a certain geometry (n\,z) condition the future set of visited sites is a key question in understanding the impact of the past on future exploration. In this talk\, I will show how to answer this question for one-dimensional self-interacting random walks ; in particular\, I will use the Brownian web to compute the distribution of future geometry (n’\, z’) given (n\, z). \nPaul Pineau: Collective Behavior of Self-Interacting Random WalkersThe collective behavior of self-interacting random walkers (SIRWs)\, also known as trail-interacting particles\, gives rise to new challenges in both physics and mathematics. The shared spatial memory generated through their deposition process leads to complex interactions and emergent phenomena. From previous studies emerge two classes of SIRWs: one in which the interaction with the deposition field saturates (commonly referred to as SATW)\, and another in which the interaction field acts as a potential that grows linearly with deposition (known as TSAW). In this talk\, I will present recent results on systems of N mutually interacting random walkers belonging to these classes. \nBalint Veto: The Brownian web distanceThe random walk web distance is a natural directed distance on the trajectory of coalescing simple random walks. It is given by the minimal number of jumps between different random walk paths when one is only allowed to move forward in time. The Brownian web distance is the scale-invariant limit of the random walk web distance which can be described in terms of the Brownian web. It is integer-valued and has scaling exponents 0:1:2 as compared to 1:2:3 in the KPZ world. The shear limit of the Brownian web distance is still given by the Airy process. A weighted version of the random walk web distance converges to a new explicit distribution that interpolates between the Gaussian and the GUE Tracy-Widom distribution. Based on joint work with Balint Virag. \nRam Adar: Active remodeling in multicellular systemsCells constantly interact with their environment through both mechanical and chemical cues. Migrating cells\, for instance\, induce irreversible local changes in the density and organization of the surrounding extracellular matrix. We refer to this process as “active remodeling”. The remodeled environment biases subsequent cellular motion and can generate new forms of collective organization and dynamics. From a theoretical perspective\, this behavior can be described by the coupled dynamics of two fields: an active field undergoing reaction-diffusion dynamics\, and an environmental field that is locally enslaved to the active field. We will illustrate this framework in two settings. First\, we will show how active remodeling alters the emergence of nematic order in active systems\, motivated by extracellular matrix remodeling by fibroblast cells. Second\, we will show how the degradation of a confining environment leads to subdiffusive dynamics and may account for the expansion rate of cancer spheroids.
URL:https://www.math.ens.psl.eu/evenement/recent-progress-on-self-interacting-processes-and-non-reversible-monte-carlo/
LOCATION:Salle W (ENS)
CATEGORIES:Programme SP(A)M!
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