Laboratoire de Physique Théorique

de la Matière Condensée

Francesco Mori (LPTMS)

Stochastic resetting: from geometric properties to optimal control

"When in a difficult situation, it is sometimes better to give up and start all over again''. While this empirical truth has been regularly observed in a wide range of circumstances, quantifying the effectiveness of such a heuristic strategy remains an open challenge. In this talk, I will first consider the minimal model of a single diffusive particle that is reset to its starting position with a constant rate. I will present recent results on the geometrical properties of this process, including the convex hull [1] and the number of visited sites [2]. Then, I will introduce a novel framework that allows to optimally control a very general class of dynamical systems through restarts [3]. This approach, analog to the celebrated Hamilton-Jacobi-Bellman equation, is successfully applied to simple settings and provides the basis to investigate realistic restarting strategies across disciplines.

[1] S. N., Majumdar, F. Mori, H. Schawe, and G. Schehr, Phys. Rev. E 103, 022135 (2021).

[2] M. Biroli, F. Mori, and S. N. Majumdar, preprint arXiv:2202.04906 (2022).

[3] B. De Bruyne and F. Mori, preprint arXiv:2112.11416 (2021).