相关论文: Non-decreasing martingale couplings

We present an in-depth study of the problem of multiple-shot discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: minimum error and unambiguous discrimination. In the case…

Given a measure $\mu$ of polynomial growth, we refine a deep result by David and Mattila to construct an atomic martingale filtration of $\mathrm{supp}(\mu)$ which provides the right framework for a dyadic form of nondoubling harmonic…

Using the calculus of variations, we prove the following structure theorem for noise stable partitions: a partition of $n$-dimensional Euclidean space into $m$ disjoint sets of fixed Gaussian volumes that maximize their noise stability must…

This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…

We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input…

We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer…

Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…

Uncertainty relations are often considered to be a measure of incompatibility of noncommuting observables. However, such a consideration is not valid in general, motivating the need for an alternate measure that applies to any set of…

This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…

We consider multimodal C^3 interval maps f satisfying a summability condition on the derivatives D_n along the critical orbits which implies the existence of an absolutely continuous f -invariant probability measure mu. If f is…

We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…

The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation…

Some exact formulae of the expectation values and probability densities in a weak measurement for an operator ${\bf A}$ which satisfies the property ${\bf A}^{2}=1$ are derived. These formulae include all-order effects of the unitary…

We investigate the behavior of the nonparametric maximum likelihood estimator $\hat{f}_n$ for a decreasing density $f$ near the boundaries of the support of $f$. We establish the limiting distribution of $\hat{f}_n(n^{-\alpha})$, where we…

Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables, which prevents us from measuring them accurately at the same time. In some applications, however, the information…

The classical correlation inequality of Harris asserts that any two monotone increasing families on the discrete cube are nonnegatively correlated. In 1996, Talagrand established a lower bound on the correlation in terms of how much the two…

We study the coupling matrix of $\mathcal{N}=2$ $SU(N)$ gauge theories with $2N$ fundamental hypermultiplets in the special vacuum, where a residual $\mathbb{Z}_N$ symmetry restores nontrivial modular structure. Using symmetry and…

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…

In this study we have computed the pair correlation functions in the two-dimensional Hubbard model using a quantum Monte Carlo method. We employ a new diagonalization algorithm in quantum Monte Carlo method which is free from the negative…