Related papers: A closure for the Master Equation starting from th…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
In these two lectures we shall discuss how the cavity approach can be used efficiently to study optimization problems with global (topological) constraints and how the same techniques can be generalized to study inverse problems in…
We study the out-of-equilibrium evolution of a strongly interacting quantum spin chain which is mapped on a system of hard rods that are coherently deposited on and removed from a lattice. We show that this closed quantum system approaches…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories…
We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses…
Evolving trees arise in many real-life scenarios from computer file systems and dynamic call graphs, to fake news propagation and disease spread. Most layout algorithms for static trees do not work well in an evolving setting (e.g., they…
The process of finding activated transitions in localized spin systems with continuous degrees of freedom is developed based on a magnetic variant of the Activation-Relaxation Technique (mART). In addition to the description of the method…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
We present a detailed derivation of the stochastic master equation determining the time evolution of the state of a general quantum system, which is placed inside a cavity and subjected to indirect measurements by monitoring the state of…
A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The…
We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do…
It has been recently shown that collisional models can be used to derive a general form for the master equations which describe the reduced time evolution of a composite multipartite quantum system, whose components "propagate" in an…
We show one possible dynamical approach to the study of the distribution of prime numbers. Our approach is based on two complexity methods, the Computable Information Content and the Entropy Information Gain, looking for analogies between…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Master equations describe the quantum dynamics of open systems interacting with an environment. They play an increasingly important role in understanding the emergence of semiclassical behavior and the generation of entropy, both being…