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Yuri Suhov

Publications and source records attributed to Yuri Suhov.

At least 19 recordsLinked to original sources
arXiv2026

Quasi-Product States and Factor Types for the One-Dimensional Hard-Core Model

We study a quasi-product state associated with the one-dimensional hard-core Gibbs measure. After coding the model by the topological Markov chain, we construct the standard path $AF$-algebra of admissible hard-core words and show that the stationary Markov measure induces on it a faithful diagonal state in the sense of Evans. We then analyze the von Neumann algebra generated by the corresponding GNS representation. The resulting algebra is a hyperfinite factor, and its type is determined by the single parameter \(\kappa=q/p^2,\) where \(\begin{pmatrix}p&q\\ 1&0\end{pmatrix}\) is the transition matrix of the Markov chain. More precisely, the factor is of type $\mathrm{II}_1$ when $\kappa =1$, and of type $\mathrm{III}_{\l}$ with \( \l=\min\{\kappa,\kappa^{-1}\}\) for $\k\neq 1$. We also specify the centralizer and the weight flow for the resulting factor.

math-ph↗
arXiv2025

Queueing models with random resetting

We introduce and study some queueing models with random resetting, including Markovian and non--Markovian models under the first-come first-served (FCFS) discipline. The Markovian models include M/M/$r$ and M/M/1+M queues with random resetting, in which a continuous-time Markov chain is formulated, with transitions including a resetting to state zero in addition to arrivals and services. We explicitly characterize the stationary distributions of the queueing processes in these models by using parting balance equations. We derive expressions for standard performance measures such as the delay probability, expected queue length and waiting time, as well as probability of a customer completing service before resetting in the M/M/$r$ model, and probability of abandonment before service or resetting in the M/M/1+M model. The non--Markovian models include GI/GI/1, GI/GI/$r$ and GI/GI/$\infty$ queues with random resetting to state zero at arrival times. For GI/GI/1 and GI/GI/$r$ queues under the FCFS discipline, we introduce modified Lindley and Kiefer--Wolfowitz recursions, respectively. Using an operator representation for these recursions, we characterize the stationary distributions via convergent series, as solutions to the modified Wiener--Hopf equations. For GI/GI/$\infty$ queues with resettings, we utilize a version of the Kiefer--Wolfowitz recursion, and also characterize the corresponding stationary distribution.

math.PR↗
arXiv2024

Context-sensitive hypothesis-testing and exponential families

We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted information and weighted entropy that proved useful in industrial/microeconomic and medical statistics. We focus on applications relevant in hypothesis testing and an analysis of exponential families. Several notions, bounds and asymptotics are established, which generalize their counterparts well-known in standard statistical research. It includes Stein-Sanov theorem, Pinsker's, Bretangnole-Huber and van Trees inequalities and Kullback--Leibler, Bhattacharya, Bregman, Burbea-Rao, Chernoff, Renyi and Tsallis divergences.

math.ST↗
arXiv2022

Birth and Death Processes in Interactive Random Environments

This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered: a continuous-time Markov chain (finite or countably infinite) and a reflected (jump) diffusion process. The background is determined by a joint Markov process carrying a specific interactive mechanism, with an explicit invariant measure whose structure is similar to a product form. We discuss a number of queueing and population-growth models and establish conditions under which the above-mentioned invariant measure can be derived. Next, an analysis of the rate of convergence to stationarity is performed for the models under consideration. We consider two settings leading to either an exponential or a polynomial convergence rate. In both cases we assume that the underlying environmental Markov process has an exponential rate of convergence, but the convergence rate of the joint Markov process is determined by certain conditions on the birth and death rates. To prove these results a coupling method turns out to be useful.

math.PR↗
arXiv2017

Weighted entropy: basic inequalities

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy power inequality for the weighted entropy and discuss connections with weighted Lieb's splitting inequality. The concepts of rates of the weighted entropy and information are also discussed.

math.PR↗
arXiv2017

Weighted entropy and optimal portfolios for risk-averse Kelly investments

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study.

math.PR↗
arXiv2016

Weighted information and entropy rates

The weighted entropy $H^{\rm w}_ϕ(X)=H^{\rm w}_ϕ(f)$ of a random variable $X$ with values $x$ and a probability-mass/density function $f$ is defined as the mean value ${\mathbb E} I^{\rm w}_ϕ(X)$ of the weighted information $I^{\rm w}_ϕ(x)=-ϕ(x)\log\,f(x)$. Here $x\mapstoϕ(x)\in{\mathbb R}$ is a given weight function (WF) indicating a 'value' of outcome $x$. For an $n$-component random vector ${\mathbf{X}}_0^{n-1}=(X_0,\ldots ,X_{n-1})$ produced by a random process ${\mathbf{X}}=(X_i,i\in{\mathbb Z})$, the weighted information $I^{\rm w}_{ϕ_n}({\mathbf x}_0^{n-1})$ and weighted entropy $H^{\rm w}_{ϕ_n}({\mathbf{X}}_0^{n-1})$ are defined similarly, with an WF $ϕ_n({\mathbf x}_0^{n-1})$. Two types of WFs $ϕ_n$ are considered, based on additive and a multiplicative forms ($ϕ_n({\mathbf x}_0^{n-1})=\sum\limits_{i=0}^{n-1}φ (x_i)$ and $ϕ_n({\mathbf x}_0^{n-1})=\prod\limits_{i=0}^{n-1}φ (x_i)$, respectively). The focus is upon ${\it rates}$ of the weighted entropy and information, regarded as parameters related to ${\mathbf{X}}$. We show that, in the context of ergodicity, a natural scale for an asymptotically additive/multiplicative WF is $\frac{1}{n^2}H^{\rm w}_{ϕ_n}({\mathbf{X}}_0^{n-1})$ and $\frac{1}{n}\log\;H^{\rm w}_{ϕ_n}({\mathbf{X}}_0^{n-1})$, respectively. This gives rise to ${\it primary}$ ${\it rates}$. The next-order terms can also be identified, leading to ${\it secondary}$ ${\it rates}$. We also consider emerging generalisations of the Shannon-McMillan-Breiman theorem.

cs.IT↗
arXiv2016

On principles of large deviation and selected data compression

The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored strings $(x_0,\ldots ,x_{n-1})\in {\mathcal X}^n$ to $\ell^{nh}$ with an arbitrary small error-probability. Here $h$ is the entropy rate of the source (calculated to the base $\ell$). We consider further reduction based on the concept of utility of a string measured in terms of a rate of a weight function. The novelty of the work is that the distribution of memory is analyzed from a probabilistic point of view. A convenient tool for assessing the degree of reduction is a probabilistic large deviation principle. Assuming a Markov-type setting, we discuss some relevant formulas, including the case of a general alphabet.

cs.IT↗
arXiv2016

On weighted Fisher information matrix properties

In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously established in [6] is given. Further, along with generalized De-Bruijn's identity, we provide new interpretation of the concavity for the entropy power.

cs.IT↗
arXiv2016

Basic inequalities for weighted entropies

The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of the weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cramér-Rao inequalities involving the weighted Fisher information matrix.

cs.IT↗
arXiv2015

An extension of the Ky Fan inequality

The aim of this paper is to analyze the weighted KyFan inequality proposed in [11]. A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an improvement of the standard KyFan inequality.

cs.IT↗
arXiv2014

Efficient Anderson localization bounds for large multi-particle systems

We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the whole of Z^N. Such bounds are proved here by means of a comprehensive fixed-energy multi-particle multi-scale analysis. Another feature of the paper is that we consider -- for the first time in the literature -- an infinite-range (although fast-decaying) interaction between particles. For the models under consideration we establish (1) exponential spectral localization, and (2) strong dynamical localization with sub-exponential rate of decay of the eigenfunction correlators.

math-ph↗
arXiv2013

Continuity of mutual entropy in the large signal-to-noise ratio limit

This article addresses the issue of the proof of the entropy power inequality (EPI), an important tool in the analysis of Gaussian channels of information transmission, proposed by Shannon. We analyse continuity properties of the mutual entropy of the input and output signals in an additive memoryless channel and discuss assumptions under which the entropy-power inequality holds true.

cs.IT↗
arXiv2010

Anderson localization for a multi-particle model with alloy-type external potential

We establish exponential localization for a multi-particle Anderson model in a Euclidean space of an arbitrary dimension, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we prove that all eigenfunctions with eigenvalues near the lower edge of the spectrum decay exponentially.

math-ph↗