Full-record statistics of one-dimensional random walks.

Abstract

We develop a comprehensive framework for analyzing full-record statistics, covering record counts M(t_{1}),M(t_{2}),..., their corresponding attainment times T_{M(t_{1})},T_{M(t_{2})},..., and the intervals until the next record. From this multiple-time distribution, we derive general expressions for various observables related to record dynamics, including the conditional number of records given the number observed at a previous time and the conditional time required to reach the current record given the occurrence time of the previous one. Our formalism is exemplified by a variety of stochastic processes, including biased nearest-neighbor random walks, asymmetric run-and-tumble dynamics, and random walks with stochastic resetting.