Related papers: The explicit form of the rate function for semi-Ma…
Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic…
We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain, defined on a locally finite weighted graph. This upper rate function is given in terms of volume growth with respect to an adapted path metric and…
The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential…
We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at $x$ decays as $1/x$ as $x \to \infty$, we quantify degree of transience via existence of moments for conditional return…
We introduce a perceptron version of the Generalized Random Energy Model, and prove a quenched Sanov type large deviation principle for the empirical distribution of the random energies. The dual of the rate function has a representation…
We investigate a new symmetry of the large deviation function of certain time-integrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but…
Letting~$N=\left\{N(t), t\geq0\right\}$ be a standard Poisson process, Stroock~ \cite{Stroock-1981} constructed a family of continuous processes by $$\Theta_{\epsilon}(t)=\int_0^t\theta_{\epsilon}(r)dr, \ \ \ \ \ 0 \le t \le 1,$$ where…
In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the…
We give a necessary and sufficient condition for a homogeneous Markov process taking values in $\R^n$ to enjoy the time-inversion property of degree $\alpha$. The condition sets the shape for the semigroup densities of the process and…
A continuous-time Markov process $X$ can be conditioned to be in a given state at a fixed time $T > 0$ using Doob's $h$-transform. This transform requires the typically intractable transition density of $X$. The effect of the $h$-transform…
In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…
We provide an exact expression for the statistics of the fluxes of Markov jump processes at all times, improving on asymptotic results from large deviation theory. The main ingredient is a generalization of the BEST theorem in enumeratoric…
We analyse the statistics of the shear stress in a one dimensional \emph{model fluid}, that exhibits a rich phase behaviour akin to real complex fluids under shear. We show that the energy flux satisfies the Gallavotti-Cohen FT across all…
We consider a standard one-dimensional Brownian motion on the time interval $[0,1]$ conditioned to have vanishing iterated time integrals up to order $N$. We show that the resulting processes can be expressed explicitly in terms of shifted…
We provide a characterization of continuous semimartingales whose law is invariant with respect to predictable random rotations. In particular we prove that all such semimartingales are obtained by integrating a predictable process with…
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as iso-kinetic and Nos\'e-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average…
In this brief paper we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for…
This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order…