4 papers
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…
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…