Related papers: Double variational principle for mean dimension wi…
Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.
We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along three main lines. First, if $d$ represents the doubling dimension of the…
We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole…
The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
Let $(X,d,f)$ be a dynamical system, where $(X,d)$ is a compact metric space and $f:X\rightarrow X$ is a continuous map. Using the concepts of \textit{g-almost product property} and \textit{uniform separation property} introduced by Pfister…
The aim of this note is to provide several variants of the diameter two properties for Banach spaces. We study such properties looking for the abundance of diametral points, which holds in the setting of Banach spaces with the Daugavet…
We consider the stationary measure of the dissipative dynamical system in a finite volume. A finite dissipation, however small, generally makes the measure singular, while at zero dissipation the measure is constant. Thus dissipative part…
We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.
Mean dimension is a topological invariant for dynamical systems that is meaningful for systems with infinite dimension and infinite entropy. Given a $\mathbb{Z}^k$-action on a compact metric space $X$, we study the following three problems…
We study random domino tilings of a multiply-connected domain with a height function defined on the universal covering space of the domain. We prove a large deviation principle for the height function in two asymptotic regimes. The first…
The dynamics of many natural systems is dominated by non-linear waves propagating through the medium. We show that the dynamics of non-linear wave fronts with positive surface tension can be formulated as a gradient system. The variational…
For dynamical systems with infinite topological entropy, the classical entropy fails to quantify their complexity effectively, while the metric mean dimension provides a natural extension in this context. In this paper, we study the…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
We develop a systematic theory for the critical phenomena with memory in all spatial dimensions, including $d<d_c$, $d=d_c$, and $d>d_c$, the upper critical dimension. We show that the Hamiltonian plays a unique role in dynamics and the…
We show that an $R^d$-topological dynamical system equipped with an invariant ergodic measure has discrete spectrum if and only it is $\mu$-mean equicontinuous (proven for $Z^d$ before). In order to do this we introduce mean equicontinuity…
We introduce the notion of Feldman-Katok metric mean dimensions in this note. We show metric mean dimensions defined by different metrics coincide under weak tame growth of covering numbers, and establish variational principles for…
Waist inequality is a fundamental inequality in geometry and topology. We apply it to the study of entropy and mean dimension of dynamical systems. We consider equivariant continuous maps between dynamical systems and assume that the mean…