## View abstract

### Session S04 - Random Walks and Related Topics

Thursday, July 15, 12:20 ~ 12:50 UTC-3

## REFINED LARGE DEVIATION PRINCIPLE FOR BRANCHING BROWNIAN MOTION CONDITIONED TO HAVE A LOW MAXIMUM

### Lisa Hartung

#### JGU Mainz, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak0f0b98fdd9fd64c176c1358cb9a95f77').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy0f0b98fdd9fd64c176c1358cb9a95f77 = 'lh&#97;rt&#117;ng' + '&#64;'; addy0f0b98fdd9fd64c176c1358cb9a95f77 = addy0f0b98fdd9fd64c176c1358cb9a95f77 + '&#117;n&#105;-m&#97;&#105;nz' + '&#46;' + 'd&#101;'; var addy_text0f0b98fdd9fd64c176c1358cb9a95f77 = 'lh&#97;rt&#117;ng' + '&#64;' + '&#117;n&#105;-m&#97;&#105;nz' + '&#46;' + 'd&#101;';document.getElementById('cloak0f0b98fdd9fd64c176c1358cb9a95f77').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy0f0b98fdd9fd64c176c1358cb9a95f77 + '\'>'+addy_text0f0b98fdd9fd64c176c1358cb9a95f77+'<\/a>';

Conditioning a branching Brownian motion to have an atypically low maximum leads to a suppression of the branching mechanism. We consider a branching Brownian motion conditioned to have a maximum below $\sqrt{2}\alpha t$ with $\alpha<1$. We study the precise effects of an early/late first branching time and a low/high first branching location under this condition. We do so by imposing additional constraints on the first branching time and location. We obtain large deviation estimates, as well as the optimal first branching time and location given the additional constraints.

Joint work with Yanjia Bai (Bonn University, Germany).