Branching Brownian motion with self repulsion
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Publication:6360555
DOI10.1007/S00023-022-01223-8zbMATH Open1510.60079arXiv2102.07128MaRDI QIDQ6360555
Publication date: 14 February 2021
Abstract: We consider a model of branching Brownian motion with self repulsion. Self-repulsion is introduced via change of measure that penalises particles spending time in an -neighbourhood of each other. We derive a simplified version of the model where only branching events are penalised. This model is almost exactly solvable and we derive a precise description of the particle numbers and branching times. In the limit of weak penalty, an interesting universal time-inhomogeneous branching process emerges. The position of the maximum is governed by a F-KPP type reaction-diffusion equation with a time dependent reaction term.
Extreme value theory; extremal stochastic processes (60G70) Reaction-diffusion equations (35K57) Brownian motion (60J65) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)
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