相关论文: Interacting Particle Systems and Jacobi Style Iden…

We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…

In this note we consider several kind of partition functions of one-dimensional models with nearest - neighbor interactions $I_n, n\in \mathbf{Z}$ and spin values $\pm 1$. We derive systems of recursive equations for each kind of such…

We claim that some non-trivial theta-function identities at higher genus can stand behind the Poisson commutativity of the Hamiltonians of elliptic integrable systems, which are made from the theta-functions on Jacobians of the…

We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state…

We consider a process in which there are p-species of particles, i.e. A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle $A_i$ can diffuse to its right neighboring site with rate $D_i$, if this site is not already…

We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of products and ratios of characteristic polynomials for random…

It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures,…

A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…

This is a short survey on recent results obtained by the authors on dynamical phase transitions of interacting particle systems. We consider particle systems with exclusion dynamics, but it is conjectured that our results should hold for a…

We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of…

A system of replicators with Hebbian random couplings is studied using dynamical methods. The self-reproducing species are here characterized by a set of binary traits and interact based on complementarity. In the case of an extensive…

Brownian particles interacting via repulsive soft-core potentials can spontaneously aggregate, despite repelling each other, and form periodic crystals of particle clusters. We study this phenomenon in low-dimensional situations (one and…

We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of arbitrary associative algebra. One is a consequence of other (fundamental identity). From the fundamental identity,…

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either…

In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…

Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The paper deals with beta Jacobi ensembles, the type with the Jacobi…

Hamiltonian formulation of N=3 systems is considered in general. The Jacobi equation is solved in three classes. Compatible Poisson structures in these classes are determined and explicitly given. The corresponding bi-Hamiltonian systems…

We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related…

We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…

A model of a device is proposed and related theoretical calculation is performed to study the weak interactions among neutral atoms and molecules. In this model 3-body collisions among the neutral particles occur repeatedly in a trap.…