Related papers: On the "Matrix Approach" to interacting particle s…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome and hard to compute, theoretical methods: (1) average Hamiltonian theory following…
We construct a four-parameter point-interaction for a non-relativistic particle moving on a line as the limit of a short range interaction with range tending toward zero. For particular choices of the parameters, we can obtain a…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
We construct matrix product steady state for a class of interacting particle systems where particles do not obey hardcore exclusion, meaning each site can occupy any number of particles subjected to the global conservation of total number…
An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…
We have introduced recently a particles model with blocking and pushing interactions which is related to a Pieri type formula for the orthogonal group. This model has a symplectic version presented here.
We prove that under a particular weak scaling, the 4-parameter interacting particle system introduced by Corwin and Petrov converges to the KPZ equation. This expands the relatively small number of systems for which weak universality of the…
The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called $\ell$-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary…
Progress in theoretical physics is often made by the investigation of toy models, the model organisms of physics, which provide benchmarks for new methodologies. For complex systems, one such model is the adaptive voter model. Despite its…
We present a concise survey of matrix completion methods and associated implementations of several fundamental algorithms. Our study covers both passive and adaptive strategies. We further illustrate the behavior of a simple adaptive…
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
We consider an exclusion process, with particles injected with rate $\alpha$ at the origin and removed with rate $\beta$ at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
We consider interacting particle systems and their mean-field limits, which are frequently used to model collective aggregation and are known to demonstrate a rich variety of pattern formations. The interaction is based on a pairwise…
In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest neighbor interactions. We consider two kinds of inter-particle interactions. In one case, the particle-hole symmetry…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
This article shows how to combine the relative entropy method by D. Bresch, P.-E. Jabin, and Z. Wang in arXiv:1706.09564, arXiv:1906.04093 and the regularized $L^2(\mathbb{R}^d)$-estimate by Oelschl\"ager (Probability theory and related…
We discuss a new method of integration over matrix variables based on a suitable gauge choice in which the angular variables decouple from the eigenvalues at least for a class of two-matrix models. The calculation of correlation functions…
The asymmetric simple exclusion process (ASEP) is a paradigm for non-equilibrium physics that appears as a building block to model various low-dimensional transport phenomena, ranging from intracellular traffic to quantum dots. We review…