First-passage-driven boundary recession. (2nd September 2022)

• Record Type: Journal Article
• Authors: De Bruyne, B; Randon-Furling, J; Redner, S
• Is Part Of: Journal of physics. Volume 55:Number 35(2022)
• Publication Date: 2022-09-02
• Subjects: first passage -- resetting -- moving boundary; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac802f
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically rich dynamics arises. In particular, the probability for the particle to first reach the moving boundary for the n th time asymptotically scales as t − ( 1 + 2 − n ) . Because the tail of this distribution becomes progressively fatter, the typical time between successive first passages systematically gets longer. We also find that the number of collisions between the particle and the boundary scales as ln ln t, while the time dependence of the boundary position varies as t /ln t .