A connection between Burgers’ equation, coagulation processes, and branching

Vortrag von Prof. Dr. Ivan Kryven

Sprecher eingeladen von: Prof. Dr. Jean Bertoin

Datum: 01.10.25  Zeit: 17.15 - 18.45  Raum: ETH HG G 43

We establish a direct correspondence between discrete‐time branching processes and a family of nonlinear evolutionary PDEs generalizing the inviscid Burgers equation. Starting from a simple nonlinear PDE, we show its stochastic analogue is a single‐type branching process with Poisson offspring, closely related to the Erdos-Renyi random graph. By relaxing the PDE’s constraints, this framework naturally extends to multitype branching processes that admit an interpretation as higher‐order coagulation with a multiplicative kernel. Our convergence analysis relies on a new large‐deviation result for the size distribution of finite progenies. Beyond providing an interesting link between PDEs and branching, the representation yields explicit bounds—and in some cases exact expressions—for the blow up time in these nonlinear PDEs.