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Session S04 - Random Walks and Related Topics

Thursday, July 15, 11:40 ~ 12:10 UTC-3

Branching Brownian motion with self-repulsion

Anton Bovier

Universität Bonn, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakae7d6af0a1bf36038174db62297ed137').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyae7d6af0a1bf36038174db62297ed137 = 'b&#111;v&#105;&#101;r' + '&#64;'; addyae7d6af0a1bf36038174db62297ed137 = addyae7d6af0a1bf36038174db62297ed137 + '&#117;n&#105;-b&#111;nn' + '&#46;' + 'd&#101;'; var addy_textae7d6af0a1bf36038174db62297ed137 = 'b&#111;v&#105;&#101;r' + '&#64;' + '&#117;n&#105;-b&#111;nn' + '&#46;' + 'd&#101;';document.getElementById('cloakae7d6af0a1bf36038174db62297ed137').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyae7d6af0a1bf36038174db62297ed137 + '\'>'+addy_textae7d6af0a1bf36038174db62297ed137+'<\/a>';

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 $\e$-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.

Joint work with Lisa Hartung (Gutenberg-University Mainz, Germany).