Winding number of a Brownian particle on a ring under stochastic resetting

Abstract We consider a random walker on ring, subjected to resetting at Poisson-distributed times the initial position (the takes shortest path along ring times). In case of Brownian mean first-completion time turn is expressed in closed form as function rate. The value shorter than ordinary process if rate low enough. Moreover, can be minimised At large distribution winding numbers does not reach steady state, which contrast with non-compact particle under real line. total number turns and variance net grow linearly time, proportionality constant equal inverse turn.