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 ...

This is a preview. Log in through your library . Abstract Some properties of the multiplicity of a class of multivariate random processes are examined with particular emphasis on the derivation of a ...

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 ...

The original version of this story appeared in Quanta Magazine. In the movie Oppenheimer, Niels Bohr challenges the physicist early in his career: Bohr: Algebra is like sheet music. The important ...

Let $X = (X_t, P^x)$ be a right Markov process and let $m$ be an excessive measure for $X$. Associated with the pair $(X, m)$ is a stationary strong Markov process ...

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 ...

Have you ever come across a statement like this: “I can’t believe that something as beautiful and complex as the human eye could be the result of a random process like evolution”? Or this: “It seems ...

Have you ever come across a statement like this: “I can’t believe that something as beautiful and complex as the human eye could be the result of a random process like evolution”? Or this: “It seems ...