Related papers: Limit Profiles for Separation Distance
The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial…
We investigate flow separation in the air flow over transverse sand dunes. CFD simulations of the air flow over differently shaped dunes are performed. The length of the recirculation region after the brink of the dune is found to depend…
Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
Information is an inherent component of stochastic processes and to measure the distance between different stochastic processes it is not sufficient to consider the distance between their laws. Instead, the information which accumulates…
We introduce and analyze the $S_k$ shuffle on $N$ cards, a natural generalization of the celebrated random adjacent transposition shuffle. In the $S_k$ shuffle, we choose uniformly at random a block of $k$ consecutive cards, and shuffle…
The paper introduces a class of distances for linear behaviors over finite time horizons. These distances allow for comparisons between finite-horizon linear behaviors represented by matrices of possibly different dimensions. They remain…
Random walk on the irreducible representations of the symmetric and general linear groups is studied. A separation distance cutoff is proved and the exact separation distance asymptotics are determined. A key tool is a method for writing…
The recent development of the massive multiple-input multiple-output (MIMO) paradigm, has been extensively based on the pursuit of favorable propagation: in the asymptotic limit, the channel vectors become nearly orthogonal and inter-user…
This work explores the clustering of wireless users by examining the distances between their channel covariance matrices, which reside on the Riemannian manifold of positive definite matrices. Specifically, we consider an estimator of the…
We study the complexity of approximations to the normalized information distance. We introduce a hierarchy of computable approximations by considering the number of oscillations. This is a function version of the difference hierarchy for…
We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes…
This work presents a data-driven framework for multi-scale parametrization of velocity-dependent dispersive transport in porous media. Pore-scale flow and transport simulations are conducted on periodic pore geometries, and volume-averaging…
We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. Also see arXiv:0707.2312 for a related paper.
This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length $N$. Our main result is that for particle densities in $(0,1),$ the total-variation cutoff window of ASEP is $N^{1/3}$ and the…
A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The…
This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued…
In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. These…
Deterministic lateral displacement (DLD) is a high-resolution separation technique used in various fields. A fundamental challenge in DLD is ensuring uniform flow characteristics across channel, particularly near sidewalls where pillar…
We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semi-flow of a deterministic differential equation which is perturbed by adding to the dynamics a white…