16 citations · 45 across the 11 of their papers we have counts for
9 papers · 1 filter
Non-uniqueness of the steady state for run-and-tumble particles with a double-well interaction potential
Léo Touzo, Pierre Le Doussal
We study run-and-tumble particles (RTPs) in one dimension interacting via a double-well potential , which is repulsive at short interparticle dis…
Exact results for active particle models: from long-range interactions to first-passage properties
Léo Touzo
The goal of this thesis is to obtain new exact results for models of active particles in one dimension, focusing on two different aspects: their behavior in the presence of long-ra…
Run-and-tumble particles with 1D Coulomb interaction: the active jellium model and the non-reciprocal self-gravitating gas
Léo Touzo, Pierre Le Doussal
Recently we studied run-and-tumble particles in one dimension - which switch with rate between driving velocities - interacting via the long range 1D Coulomb pote…
Crystal to liquid cross-over for active particles with inverse-square power-law interaction
Saikat Santra, Leo Touzo, Chandan Dasgupta +6
We consider a one-dimensional system comprising of run-and-tumble particles confined in a harmonic trap interacting via a repulsive inverse-square power-law interaction. We num…
Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
Mathis Guéneau, Léo Touzo
We consider a generic one-dimensional stochastic process , or a random walk , which describes the position of a particle evolving inside an interval , with absorb…
Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle
Mathis Guéneau, Léo Touzo
The connection between absorbing boundary conditions and hard walls is well established in the mathematical literature for a variety of stochastic models, including for instance th…
Non-equilibrium phase transitions in active rank diffusions
Léo Touzo, Pierre Le Doussal
We consider N run and tumble particles in one dimension interacting via a linear 1D Coulomb potential, an active version of the rank diffusion problem. It was solved previously for…
Fluctuations in the active Dyson Brownian motion and the overdamped Calogero-Moser model
Leo Touzo, Pierre Le Doussal, Gregory Schehr
Recently, we introduced the active Dyson Brownian motion model (DBM), in which run-and-tumble particles interact via a logarithmic repulsive potential in the presence of a harm…
Interacting, running and tumbling: the active Dyson Brownian motion
Leo Touzo, Pierre Le Doussal, Gregory Schehr
We introduce and study a model in one dimension of run-and-tumble particles (RTP) which repel each other logarithmically in the presence of an external quadratic potential. Thi…