相关论文: Concentration inequalities for sequential dynamica…
High-dimensional compartmental dynamical systems have been introduced to model brain metabolism. In this article, an approach is proposed to their mathematical analysis. Reductions of these models are obtained by replacing several…
The coherent dynamics of bubble clusters in liquid are of fundamental and industrial importance and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate unsupervised learning of…
We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those defining the almost-supermartingale processes introduced by…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We introduce behavioral inequalities as a way to model dynamical systems defined by inequalities among their variables of interest. We claim that such a formulation enables the representation of safety-aware dynamical systems, systems with…
This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $\beta N \to const \in (0, \infty)$, with $N$ the system size and $\beta$ the inverse temperature. In this regime, the convergence to…
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a…
In this paper we study time semi-discrete approximations of a class of exponentially stable infinite dimensional systems with unbounded feedbacks. It has recently been proved that for time semi-discrete systems, due to high frequency…
One of the fundamental eigenmodes of finite interacting systems is the mode of {\em uniform radial expansion and contraction} -- the ``breathing'' mode (BM). Here we show in a general way that this mode exists only under special conditions:…
We consider a particle moving in one dimension, its velocity being a reversible diffusion process, with constant diffusion coefficient, of which the invariant measure behaves like $(1+|v|)^{-\beta}$ for some $\beta>0$. We prove that, under…
The propagation and decay of neutral B-mesons can be described in terms of quantum dynamical semigroups; they provide generalized time-evolutions that take into account possible non-standard effects leading to loss of phase coherence and…
We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the…
In previous papers we have introduced a sufficient condition for uniform attractivity of the origin for a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the…
In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…
This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…
We consider a chain of Euler-Bernoulli beams with spatial dependent mass density, modulus of elasticity and area moment which are interconnected in dissipative or conservative ways and prove uniform exponential energy decay of the coupled…
Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these…
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 study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the…
Defining the density flow of perturbations moving at a given speed for cellular automata, we establish equalities and inequalities between the measurable entropy of a cellular automaton and the measurable entropy of its associated shift.