Related papers: Finite time large deviations via matrix product st…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given…
We introduce a stochastic generalisation of the classical deterministic Floquet-East model, a discrete circuit with the same kinetic constraint as the East model of glasses. We prove exactly that, in the limit of long time and large size,…
Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can…
Finite state machines (FSMs) are a theoretically and practically important model of computation. We propose a general, thermodynamically consistent model of FSMs and characterise the resource requirements of these machines. We model FSMs as…
We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
This paper studies the exponential stability of random matrix products driven by a general (possibly unbounded) state space Markov chain. It is a cornerstone in the analysis of stochastic algorithms in machine learning (e.g. for parameter…
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the…
One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
We consider ensembles of trajectories associated with large deviations of time-integrated quantities in stochastic models. Motivated by proposals that these ensembles are relevant for physical processes such as shearing and glassy…
Matrix models have phase transitions in which distributions of variables change topologically like the Gross-Witten-Wadia transition. In a recent study, similar splitting-merging behavior of distributions of dynamical variables was observed…
For diffusion processes in dimension $d>1$, the statistics of trajectory observables over the time-window $[0,T]$ can be studied via the Feynman-Kac deformations of the Fokker-Planck generator, that can be interpreted as euclidean…