Seminario di Probabilità

Martedì 21 ottobre alle ore 16:00, Maike de Jongh (University of Twente), terrà il seminario di probabilità dal titolo "Controlling the zero-temperature Ising model using Markov decision theory".

Abstract: The behavior of the Ising model under external control mechanisms is of interest in a wide variety of applications, including biological systems, social dynamics, and information processing. In this talk, we investigate control strategies for a zero-temperature two-dimensional Ising model on a finite square lattice evolving under Metropolis dynamics. Specifically, we consider a situation in which an external controller aims to drive the system from a configuration with a small droplet of +-spins towards the all-plus configuration by flipping spins at specific sites at predetermined moments in time. In order to analyze this control problem, we formulate it as a Markov decision process (MDP), a well-established framework for sequential decision-making problems under uncertainty. To find an optimal policy in this MDP, we construct a simplified model by means of a reduction of the configuration space to the local minima of the Hamiltonian. Leveraging the convenient form of this simplified model, we uncover the structure of the optimal policy by solving the Bellman equations in a recursive manner. Finally, we present simulation results illustrating the performance of this optimal policy in the original control problem at low temperatures.

Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica. Via della Vasca Navale, 84 - Aula F