Related papers: Sofic Entropy of Gaussian Actions

We show that if G is a discrete group which does not have the Haagerup property but does have an unbounded cocycle into a C_0 representation and if G acts on a finite von Neumann algebra B such that the inclusion B \subset (B \rtimes G) has…

The purpose of this work is to bound sofic topological entropy of Toeplitz systems over residually finite groups and to prove the Krieger Theorem about attaining arbitrary entropy by the Toeplitz systems. To achieve these results, we…

We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy…

In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and…

We consider random walks on finitely or countably generated free semigroups, and identify their Poisson boundaries for classes of measures which fail to meet the classical entropy criteria. In particular, we introduce the notion of…

Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…

We show that the theory of Galois actions of a torsion Abelian group $A$ is companionable if and only if for each prime $p$, the $p$-primary part of $A$ is either finite or it coincides with the Pr\"{u}fer $p$-group. We also provide a…

Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically distributed) processes (a.k.a. product measures). This theory holds for amenable groups as well.…

A measure preserving action of a countably infinite group \Gamma is called totally ergodic if every infinite subgroup of \Gamma acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if…

A new type of non-Abelian generalization of the Born-Infeld action is proposed, in which the spacetime indices and group indices are combined. The action is manifestly Lorentz and gauge invariant. In its power expansion, the lowest order…

We propose a method for computing the Kolmogorov-Sinai (KS) entropy of chaotic systems. In this method, the KS entropy is expressed as a statistical average over the canonical ensemble for a Hamiltonian with many ground states. This…

We use two non-perturbative methods to obtain the anisotropy derivatives of the coupling constants (the anisotropy coefficients) of SU(3) lattice gauge theory. These coefficients appear in the derivative formulae for the energy density and…

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian Boson Sampling, where quadratic photonic input states are…

Given an ergodic probability preserving flow $T=(T_t)_{t\in\Bbb R}$, let $I(T):=\{s\in\Bbb R^*\mid T\text{is isomorphic to}(T_{st})_{t\in\Bbb R}\}$. A weakly mixing Gaussian flow $T$ is constructed such that $I(T)$ is uncountable and…

Let G be a closed subgroup of the group of all permutations of a countably infinite set. Let X be a Polish G-space with a countable basis A of clopen sets. Each x from X defines a characteristic function f on A by f(U)=1 iff x belongs to U…

This is a survey of work in which the author was involved in recent years. We consider C*-algebras constructed from representations of one or several algebraic endomorphisms of a compact abelian group - or, dually, of a discrete abelian…

We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…

Mobility entropy is proposed to measure predictability of human movements, based on which, the upper and lower bound of prediction accuracy is deduced, but corresponding mathematical expressions of prediction accuracy keeps yet open. In…

Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…

We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…