Related papers: Singularity of compound stationary measures
The analytic properties of the Markov operator associated to a random walk are common tools in the study of the behaviour and some probabilistic features related to the walk. In this paper we consider a class of Markov operators which…
We explore the Lyapunov spectrum and entanglement entropy in systems evolved by quantum measurements and spatially homogeneous unitary gates. In models with temporally random and Floquet unitary gates, we find that the Lyapunov exponents…
We propose a notion of conditioned stochastic stability of invariant measures on repellers: we consider whether quasi-ergodic measures of absorbing Markov processes, generated by random perturbations of the deterministic dynamics and…
The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second…
We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…
Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…
We take the point of view of a particle performing random walk with bounded jumps on $\mathbb{Z}^d$ in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the…
In this paper we study ergodic optimization problems for typical cocycles. We consider one-step $SL(2,\mathbb{R})$-cocycles that satisfy pinching and twisting conditions. We prove that the Lyapunov maximizing measures have zero entropy…
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…
In [4], we examined the use of coupling to obtain bounds on the mixing time of statistics on Markov chains. In the present paper, we consider the same general problem, but using strong stationary times rather than coupling. We discuss…
We study the asymptotic behavior of Markov operators $P_\mu$ defined by convolution with a probability measure $\mu$ on the unit circle $\mathbb T$. We prove that when $\mu$ is adapted, $P_\mu$ satisfies Doeblin's condition if and only if…
If moments of singular measures are passed as inputs to the entropy maximization procedure, the optimization algorithm might not terminate. The framework developed in our previous paper demonstrated how input moments of measures, on a broad…
Previous work has separately addressed different forms of action, state and action-state entropy regularization, pure exploration and space occupation. These problems have become extremely relevant for regularization, generalization,…
We continue the analysis of nontrivial examples of quantum Markov processes. This is done by applying the construction of entangled Markov chains obtained from classical Markov chains with infinite state--space. The formula giving the joint…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…
The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…
We study the decay of convolution powers of a large family $\mu_{S,a}$ of measures on finitely generated nilpotent groups. Here, $S=(s_1,...,s_k)$ is a generating $k$-tuple of group elements and $a= (\alpha_1,...,\alpha_k)$ is a $k$-tuple…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…
Markov combination is an operation that takes two statistical models and produces a third whose marginal distributions include those of the original models. Building upon and extending existing work in the Gaussian case, we develop Markov…