Related papers: Multiple correlation sequences and nilsequences
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following…
The behavior of correlation functions is studied in a class of matrix models characterized by a measure $\exp(-S)$ containing a potential term and an external source term: $S=N\tr(V(M)-MA)$. In the large $N$ limit, the short-distance…
Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…
Wall-crossing phenomena are ubiquitous in many problems of algebraic geometry and theoretical physics. Various ways to encode the relevant information and the need to track the changes under the variation of parameters lead to rather…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
Ensemble algorithms offer state of the art performance in many machine learning applications. A common explanation for their excellent performance is due to the bias-variance decomposition of the mean squared error which shows that the…
Clustering evaluation measures are frequently used to evaluate the performance of algorithms. However, most measures are not properly normalized and ignore some information in the inherent structure of clusterings. We model the relation…
Motion correlation interfaces are those that present targets moving in different patterns, which the user can select by matching their motion. In this paper, we re-formulate the task of target selection as a probabilistic inference problem.…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
We investigate the convergence behavior of the extended dynamic mode decomposition for constructing a discretization of the continuity equation associated with the Lorenz equations using a nonlinear dictionary of over 1,000,000 terms. The…
Given a uniformly convergent sequence of ambient isotopies $(H_n)_{n\in\mathbb{N}}$, bijectivity of the limit function $H_\infty$ together with a minor compactness condition guarantees that $H_\infty$ is also an ambient isotopy. By…
We give an operadic interpretation of the known result of L.Shapiro and A.B.Stephens that characterizes percolating permutation matrices. A relation of ideals and suboperads of the non-symmetric operad of permutations to percolative…
In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone…
The correlation measure is a testimony of the pseudorandomness of a sequence $\infw{s}$ and provides information about the independence of some parts of $\infw{s}$ and their shifts. Combined with the well-distribution measure, a sequence…
We study the discrete dynamical system obtained by repeatedly applying the Pearson correlation operator to a real matrix. Each step centers every row, normalizes each centered row to unit Euclidean norm, and forms the Gram matrix of the…
We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such…
We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may…
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped…