CRM: Centro De Giorgi
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Regular and Stochastic Behaviour in Dynamical Systems

Effects of resetting on stochastic search processes with finite or infinite lifetime

speaker: Mattia Radice (Max Planck Institute for the Physics of Complex Systems)

abstract: Stochastic resetting is a simple mechanism by which from time to time a random process is restored to a given condition, usually corresponding to the initial state. Following each resetting event the dynamics is started anew, with loss of memory of the previous history. Despite the simplicity of the mechanism, the repeated returns to a given location produce non-trivial effects on the statistical properties of the dynamics. In this talk I will focus on the effects of resetting on the first-passage properties of a stochastic process. More specifically, I will discuss how resetting affects the statistics of the first-passage time, namely the random variable describing the time to reach a specific state (which, in practical problems, often corresponds to the position of a target) for the first time. First, I will briefly review the most important results on the subject, showing in particular how resetting can actually speed up the search process. Then, I will show that the problem changes radically if the process subjected to restart has a finite lifetime, i.e. if it can stop before reaching the target. Situations like this are ubiquitous in nature and occur, for example, whenever we describe an object subject to a natural decay process. In such cases, resetting not only has an impact on the first-passage properties, but also on the probability of successfully completing the search before the process is stopped (i.e., before the particle “decays”), hence the problem becomes much less trivial. I will explain how different situations arise depending on the relative magnitude of the time scales describing the average lifetime of the process and the mean time between two resetting events, specifying in which resetting may still be advantageous and in which it should be avoided.

Tue 6 Jun, 14:30 - 15:30, Aula Dini
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