Related papers: Gap distributions and homogeneous dynamics
We analyse the Langevin dynamics of the random walk, the scalar field, the X-Y model and the spinoidal decomposition. We study the deviations from the equilibrium dynamics theorems (FDT and homogeneity), the asymptotic behaviour of the…
The analysis of network dynamics is oftentimes restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between behavior of systems with one-dimensional internal dynamics and with…
We study the group theoretical properties of the Lame equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical symmetry limits.
Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the $L^2$-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the…
We study analytically and numerically the statics and the off-equilibrium dynamics of spin models over finitely connected random graphs. We identify a threshold value for the connectivity beyond which the loop structure of the graph becomes…
This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role…
In this report I present a possible scenario which can lead to the emergence of a generalised Gamma distribution first presented by R. Osorio et al. as the distribution of traded volumes of stocks in financial markets. This propose is…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…
We study the dynamical large deviations of the classical stochastic symmetric simple exclusion process (SSEP) by means of numerical matrix product states. We show that for half-filling, long-time trajectories with a large enough imbalance…
We introduce a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. Motivated by models of regulatory networks, we construct a state transition graph from a piecewise affine…
We consider networks made of parallel lanes along which particles hop according to driven diffusive dynamics. The particles also hop transversely from lane to lane, hence indirectly coupling their longitudinal dynamics. We present a general…
Logit dynamics is a form of randomized game dynamics where players have a bias towards strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics…
We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…