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We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…
In this paper we take the first step toward a classification of the approximation complexity of the six-vertex model, an object of extensive research in statistical physics. Our complexity results conform to the phase transition phenomenon…
The Curie-Weiss model is used to study phase transitions in statistical mechanics and has been the object of rigorous analysis in mathematical physics. We analyse the problem of reconstructing the probability measure of a multi-group…
A surrogate model for particle-in-cell plasma simulations based on a graph neural network is presented. The graph is constructed in such a way as to enable the representation of electromagnetic fields on a fixed spatial grid. The model is…
A practical and accessible introduction to most probable phase portraits is given. The reader is assumed to be familiar with stochastic differential equations and Euler-Maruyama method in numerical simulation. The article first introduce…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
We derive a simple expression for the probability of trajectories of a master equation. The expression is particularly useful when the number of states is small and permits the calculation of observables that can be defined as functionals…
We propose a simple model for a binary decision making process on a graph, motivated by modeling social decision making with cooperative individuals. The model is similar to a random field Ising model or fiber bundle model, but with key…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
We develop a class of exponential-family point processes based on a latent social space to model the coevolution of social structure and behavior over time. Temporal dynamics are modeled as a discrete Markov process specified through…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for…
Consider the complete graph \(K_n\) on \(n\) vertices where each edge \(e\) is independently open with probability \(p_n(e)\) or closed otherwise. Here \(\frac{C-\alpha_n}{n} \leq p_n(e) \leq \frac{C+\alpha_n}{n}\) where \(C > 0\) is a…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
We suggest a new Bayesian analysis using disjunct M-R constraints for extracting probability measures for cold, dense matter equations of state. One of the key issues of such an analysis is the question of a deconfinement transition in…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…