5 papers
Higher order asymptotics for the nonlinear Schrödinger equation
Jiaqi Liu, Changhua Yang
In this paper we compute the higher order long time asymptotics of the defocussing nonlinear Schrödinger equation using the -nonlinear steepest descent method.…
Inverting the operation of conditioning a branching process on extinction
Ewain Gwynne, Jiaqi Liu
It is well-known that conditioning a supercritical (multi-type) branching process on the event that it eventually becomes extinct yields a subcritical branching process. We study t…
The Yaglom limit for branching Brownian motion with absorption and slightly subcritical drift
Julien Berestycki, Jiaqi Liu, Bastien Mallein +1
Consider branching Brownian motion with absorption in which particles move independently as one-dimensional Brownian motions with drift , each particle splits into two particle…
Phase transition of the consistent maximal displacement of branching Brownian motion
Julien Berestycki, Jiaqi Liu, Bastien Mallein +1
Consider branching Brownian motion in which we begin with one particle at the origin, particles independently move according to Brownian motion, and particles split into two at rat…
Critical drift estimates for the frog model on trees
Emma Bailey, Matthew Junge, Jiaqi Liu
Place an active particle at the root of a -ary tree and a single dormant particle at each non-root site. In discrete time, active particles move towards the root with probabilit…