Related papers: Mutual Dimension and Random Sequences
A data processing inequality states that the quantity of shared information between two entities (e.g. signals, strings) cannot be significantly increased when one of the entities is processed by certain kinds of transformations. In this…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
Obtaining the exact multi-time correlations for one-dimensional growth models described by the Kardar-Parisi-Zhang (KPZ) universality class is presently an outstanding open problem. Here, we study the joint probability distribution function…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…
We investigate a relationship network of humans located in a metric space where relationships are drawn according to a distance-dependent probability density. The obtained spatial graph allows us to calculate the average separation of…
The Fuzz programming language [Reed and Pierce, 2010] uses an elegant linear type system combined with a monad-like type to express and reason about probabilistic sensitivity properties, most notably $\epsilon$-differential privacy. We show…
We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…
This paper studies the universal approximation property of deep neural networks for representing probability distributions. Given a target distribution $\pi$ and a source distribution $p_z$ both defined on $\mathbb{R}^d$, we prove under…
We propose a solution to the puzzle of dimensional reduction in the random field Ising model, inverting the question and asking: to what random problem in $D=d+2$ dimensions does a pure system in $d$ dimensions correspond? We consider two…
While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…
Two-sample tests are important areas aiming to determine whether two collections of observations follow the same distribution or not. We propose two-sample tests based on integral probability metric (IPM) for high-dimensional samples…
Hardy's paradox is of fundamental importance in quantum information theory. So far, there have been two types of its extensions into higher dimensions: in the first type the maximum probability of nonlocal events is roughly $9\%$ and…
We study popular matchings in three classical settings: the house allocation problem, the marriage problem, and the roommates problem. In the popular matching problem, (a subset of) the vertices in a graph have preference orderings over…
The characteristics of data like distribution and heterogeneity, become more complex and counterintuitive as dimensionality increases. This phenomenon is known as curse of dimensionality, where common patterns and relationships (e.g.,…
Three measures of pseudorandomness of finite binary sequences were introduced by Mauduit and S\'ark\"ozy in 1997 and have been studied extensively since then: the normality measure, the well-distribution measure, and the correlation measure…
Let R be a commutative noetherian local ring, and M a finitely generated R-module of infinite projective dimension. It is well-known that the depths of the syzygy modules of M eventually stabilize to the depth of R. In this paper, we…
Mutual information I in infinite sequences (and in their finite prefixes) is essential in theoretical analysis of many situations. Yet its right definition has been elusive for a long time. I address it by generalizing Kolmogorov Complexity…
Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…
Neural networks with random weights appear in a variety of machine learning applications, most prominently as the initialization of many deep learning algorithms and as a computationally cheap alternative to fully learned neural networks.…