Random walks and percolation theory form a fundamental confluence in modern statistical physics and probability theory. Random walks describe the seemingly erratic movement of particles or entities, ...

Percolation theory examines the emergence of connected clusters in systems composed of randomly occupied sites or bonds, making it an invaluable framework for understanding phase transitions in ...

We study the heat kernel and the Green’s function on the infinite supercritical percolation cluster in dimension d ≥ 2 and prove a quantitative homogenization theorem for these functions with an ...

With Hugo Duminil-Copin, thinking rarely happens without moving. His insights into the flow-related properties of complex networks have earned him the Fields Medal. The math department at the ...