Related papers: A note on uniform in time mean-field limit in grap…
We propose a model of card shuffling where a pack of cards, spread as points on a square table, are repeatedly gathered locally at random spots and then spread towards a random direction. A shuffling of the cards is then obtained by…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
The perceived randomness in the time evolution of "chaotic" dynamical systems can be characterized by universal probabilistic limit laws, which do not depend on the fine features of the individual system. One important example is the…
The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation in the presence of a convex external potential, without smallness restriction on the interaction. From this are…
In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the $N$-particle Newtonian system. For $L^1\cap L^\infty$ initial data, the solvability of the mean field kinetic equation can…
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent…
We consider a synchronous process of particles moving on the vertices of a graph $G$, introduced by Cooper, McDowell, Radzik, Rivera and Shiraga (2018). Initially, $M$ particles are placed on a vertex of $G$. In subsequent time steps, all…
The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
We study the connection between mixing properties for bipartite graphs and materialization of the mutual information in one-shot settings. We show that mixing properties of a graph imply impossibility to extract the mutual information…
The interplay between different types of disorder and electron-electron interactions in graphene planes is studied by means of Renormalization Group techniques. The low temperature properties of the system are determined by fixed points…
In this article we study a system of $N$ particles, each of them being defined by the couple of a position (in $\mathbb{R}^d$) and a so-called orientation which is an element of a compact Riemannian manifold. This orientation can be seen as…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
The delay experienced by a probe due to interactions with a scattering media is highly related to the internal dynamics inside that media. This property is well captured by the Wigner delay time and the resonance widths. By the use of the…
We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show convergence of the…
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…
In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…