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 ...

For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These ...

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 ...

Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

A random variable is a mathematical function that maps outcomes of random experiments to numbers. It can be thought of as the numeric result of operating a non-deterministic mechanism or performing a ...