the laplace operator is the infinitesimal generator of brownian motion with a real state space.  the vladimirov operator, a $p$-adic analogue of the laplace operator, similarly gives rise to brownian motion with a $p$-adic state space.  this talk aims to introduce the concept of a $p$-adic brownian motion and demonstrate a further similarity with its real analogue: $p$-adic brownian motion is a scaling limit of a discrete-time random walk on a discrete group.  attendees need not have prior knowledge of $p$-adic analysis, as the talk will provide a brief review of necessary background information.