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 ...

Branching processes in random environments constitute a significant class of stochastic models designed to capture the interplay between intrinsic reproductive dynamics and extrinsic environmental ...

CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

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 ...

Silicon photonics is rapidly emerging as a promising technology to enable higher bandwidth, lower energy, and lower latency communication and information processing, and other applications. In silicon ...

Silicon photonics uses existing CMOS manufacturing infrastructure and techniques but lacks mature models that take into account known CMOS process variations and their effect on photonic component ...

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 ...