10 papers
Uniform-in-time propagation of chaos for singular interaction kernels with rates
Nicoleta Cazacu, Alexandre Richard, Milica Tomasevic
Based on a semigroup approach, we prove quantitative uniform-in-time propagation of chaos for two systems of interacting particles with singular interaction kernels of type $L^…
Asymptotics of a two-species particle system associated to the doubly parabolic Keller-Segel equation in the plane
Nicolas Fournier, Milica Tomašević
We consider the two-species particle system introduced by Stevens (2000) related to the doubly parabolic Keller-Segel equation. It consists of cells and of a varying number of…
Growing random planar network with oriented branching and fusion
Vincent Bansaye, Gael Raoul, Milica Tomasevic
We consider a growing planar network where a tip grows at constant speed, branches at constant rate and inactivates when it meets a branch already created. We only consider here or…
Quantitative approximation of a Keller--Segel PDE by a branching moderately interacting particle system and suppression of blow-up
Thomas Cavallazzi, Alexandre Richard, Milica Tomasevic
The Keller--Segel PDE is a model for chemotaxis known to exhibit possible finite-time blow-up. Following a seminal work by Tello and Winkler, a logistic damping term is added in th…
Convergence and Wave Propagation for a System of Branching Rank-Based Interacting Brownian Particles
Mete Demircigil, Milica Tomasevic
In this work we study a branching particle system of diffusion processes on the real line interacting through their rank in the system. Namely, each particle follows an independent…
Curvature in chemotaxis: A model for ant trail pattern formation
Charles Bertucci, Matthias Rakotomalala, Milica Tomasevic
In this paper, we propose a new model of chemotaxis motivated by ant trail pattern formation, formulated as a coupled parabolic-parabolic local PDE system, for the population densi…
Long-time behaviour of a multidimensional age-dependent branching process with a singular jump kernel modelling telomere shortening
Jules Olayé, Milica Tomasevic
In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of tel…
Mean-field limit of particle systems with absorption
Gaoyue Guo, Maxime Latypov, Milica Tomasevic
In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are remov…
Propagation of chaos for stochastic particle systems with singular mean-field interaction of type
Milica Tomašević
In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belon…
On a multi-dimensional McKean-Vlasov SDE with memorial and singular interaction associated to the parabolic-parabolic Keller-Segel model
Milica Tomašević, Guillaume Woessner
In this work we firstly prove the well-posedness of the non-linear martingale problem related to a McKean-Vlasov stochastic differential equation with singular interaction kernel i…