Related papers: Large deviations and adiabatic transitions for dyn…
The averaged dynamics of various two-phase systems in a high-frequency vibration field is studied theoretically. The continuum approach is applied to describe such systems as solid particle suspensions, emulsions, bubbly fluids, when the…
This work studies the averaging principle for a fully coupled two time-scale system, whose slow process is a diffusion process and fast process is a purely jumping process on an infinitely countable state space. The ergodicity of the fast…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…
We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by…
Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with $L_2$ semigroups under minimal conditions on the state space and the process trajectories; for example, no strong…
Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are…
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…
We study dynamical phase transitions in a model supercooled liquid. These transitions occur in ensembles of trajectories that are biased towards low (or high) dynamical activity. We compare two different measures of activity that were…
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables…
This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…