If $d$ is a fixed positive integer, let $\Lambda_N$ be a finite subset of $Z^d$, the lattice points of $\mathbb{R}^d$, with $\Lambda_N \uparrow Z^d$ and satisfying ...

Some invariance principles for additive functionals of simple exclusion with finite-range translation-invariant jump rates p(i, j) = p(j − i) in dimensions d ≥ 1 are established. A previous ...

Random fields provide a versatile mathematical framework to describe spatially dependent phenomena, ranging from physical systems and quantum chaos to cosmology and spatial statistics. Underpinning ...

Random walks constitute one of the cornerstone concepts in probability theory and statistical physics, representing a class of stochastic processes in which a moving entity takes successive steps in ...