Alan Hammond

Biased random walks on Galton–Watson trees with leaves

We consider a biased random walk

Kinetic Limit for a System of Coagulating Planar Brownian Particles

X_n

Local time on the exceptional set of dynamical percolation and the incipient infinite cluster

on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant

Stable limit laws for randomly biased walks on supercritical trees

\gamma= \gamma(\beta) \in (0,1)

Phase separation in random cluster models II: The droplet at equilibrium, and local deviation lower bounds

, depending on the bias

Greedy lattice animals: Geometry and criticality

\beta

On the probability that self-avoiding walk ends at a given point

, such that

FLUCTUATION OF A PLANAR BROWNIAN LOOP CAPTURING A LARGE AREA

X_n

An upper bound on the number of self-avoiding polygons via joining

is of order

Coagulation and diffusion: A probabilistic perspective on the Smoluchowski PDE

n^{\gamma}