From the 1 of 6 linked papers with an AI index.
6 papers
Exact collective first-passage statistics of N trail-interacting walkers
Paul Pineau, Julien Brémont, Olivier Bénichou +1
The paper derives exact formulas for the first‑passage times and splitting probabilities of N one‑dimensional random walkers that interact through a shared, persistent trail field,…
Aging Record Statistics in Saturating Self-Interacting Random Walks
J. Brémont, R. Voituriez, O. Bénichou
The record age tau_k, defined as the time between the k-th and k+1-st record-breaking events, is a central observable of extreme-value statistics. In Markovian processes, the absen…
Beyond Poisson: First-Passage Asymptotics of Renewal Shot Noise
Julien Brémont
The first-passage time (FPT) of a stochastic signal to a threshold is a fundamental observable across physics, biology, and finance. While renewal shot noise is a canonical model f…
Exploration and aging of non-Markovian processes
Julien Brémont
This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influe…
Flips Reveal the Universal Impact of Memory on Random Explorations
Julien Brémont, Léo Régnier, Alex Barbier--Chebbah +2
Quantifying space exploration is a central question in random walk theory, with direct applications ranging from animal foraging, diffusion-limited reactions, and intracellular tra…
Persistence exponents of self-interacting random walks
Julien Brémont, Léo Régnier, Olivier Bénichou +1
The persistence exponent, which characterises the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in qu…