Random walks constitute a foundational concept in probability theory, describing the seemingly erratic movement of particles or agents as they traverse a space in a series of stochastic steps. In many ...

A critical branching process {Zk, k = 0, 1, 2,...} in a random environment is considered. A conditional functional limit theorem for the properly scaled process {log Zpu, 0 ≤ u < ∞} is established ...

Tiny particles like pollen grains move constantly, pushed and pulled by environmental forces. To study this motion, physicists use a “random walk” model — a system in which every step is determined by ...

A mathematician who developed formulas to make random processes more predictable and helped to solve an iconic model of complex phenomena has won the 2024 Abel Prize, one of the field’s most coveted ...