Voting models on branching random walks

by Xaver Kriechbaum (IMT)

Tuesday Sep 9, 2025, 9:50 AM → 10:50 AM Europe/Paris

Amphi Schwartz

We consider recursion equations of the form u_{n+1}(x)=g(u_n∗q), where g is a polynomial, satisfying g(0)=0, g(1)=1, g((0,1))⊆(0,1), and q is a (compactly supported) probability density with ∗ denoting convolution. These are discrete analogues of KPP type equations. Motivated by a line of works for nonlinear PDEs initiated by Etheridge, Freeman and Penington (2017), we show for which polynomials g the family (u_n)_{n\in\mathbb{N}} can be represented via voting models on branching random walks. We use this connection to describe the geometry of the (u_n) for a class of models: we will show that on a macroscopic level, u_n has finitely many jumps and is otherwise flat, the jumps can be isolated to intervals of finite-in-n length. 

The talk is based on joined work with Lenya Ryzhik and Ofer Zeitouni.