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 ...

Stochastic processes form the backbone of modern probability theory, describing systems that evolve randomly over time or space. They are instrumental in areas ranging from statistical physics to ...

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 ...

Victor Chernozhukov, Denis Chetverikov, Kengo Kato, 2017, Annals of Probability 今回は、Chernozhukov・Chetverikov・加藤による 「Central Limit Theorems and Bootstrap in High Dimensions」(2017) ...

Limit theorems are proved for two stochastic models of molecular evolution in finite populations of fixed size. An additive fitness model is shown to be asymptotically neutral in the sense that the ...