Related papers: Infinite particle systems of long range jumps with…
We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting…
Firstly we consider a finite dimensional Markov semigroup generated by Dunkl laplacian with drift terms. Using gradient bounds we show that for small coefficients this semigroup has an invariant measure. We then extend this analysis to an…
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method…
We analyze the properties of the contact process with long-range interactions by the use of a kinetic ensemble in which the total number of particles is strictly conserved. In this ensemble, both annihilation and creation processes are…
A stochastic dynamics $({\bf X}(t))_{t\ge0}$ of a classical continuous system is a stochastic process which takes values in the space $\Gamma$ of all locally finite subsets (configurations) in $\Bbb R$ and which has a Gibbs measure $\mu$ as…
This note is a companion article to the recent paper L\"ocherbach, Loukianova, Marini (2024). We consider mean field systems of interacting particles. Each particle jumps with a jump rate depending on its position. When jumping, a…
Non-colliding Brownian particles in one dimension is studied. $N$ Brownian particles start from the origin at time 0 and then they do not collide with each other until finite time $T$. We derive the determinantal expressions for the…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
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…
For any system $\{i\}$ of particles with the trajectories $x_{i}(t)$ in $R^{d}$ on a finite time interval $[0,\tau]$ we define the interaction graph $G$. Vertices of $G$ are the particles, there is an edge between two particles $i,j$ iff…
Aggregation of like-charged polymers is widely observed in biological and soft matter systems. In many systems, bundles are formed when a short-range attraction of diverse physical origin like charge-bridging, hydrogen-bonding or…
We consider a particle system on $\mathbb{Z}^d$ with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture…
For finite interacting particle systems with strong repulsing-attracting or general interactions, we prove global weak well-posedness almost up to the critical threshold of the strengths of attracting interactions (independent of the number…
We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…
We study the long-time behavior of two run-and-tumble particles on the real line subjected to an attractive interaction potential and jamming interactions, which prevent the particles from crossing. We provide the explicit invariant…
Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Fermi particles by long-rage forces, and we demonstrated nonperturbative calculation of the partition…
This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the…
We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisions in the grazing regime, and happens to be a special…
In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a…
We consider a system of N classical particles, interacting via a smooth, short- range potential, in a weak-coupling regime. This means that N tends to infinity when the interaction is suitably rescaled. The j-particle marginals, which obey…