Related papers: Limit Profiles for Separation Distance
In this thesis we introduce a new type of card shuffle called the one-sided transposition shuffle. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniformly from below it. This defines a…
This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on…
We present a method to estimate the segregation parameter, $S,$ a key input in a continuum transport model of particulate flows. $S$ is determined by minimizing the difference between measured and model-predicted concentration profiles. To…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
We study the speed of convergence to equilibrium for the asymmetric simple exclusion process (ASEP) on a finite interval with one open boundary. We provide sharp estimates on the total-variation distance from equilibrium and verify that the…
Transportation distance information is a powerful resource, but location records are often censored due to privacy concerns or regulatory mandates. We outline methods to approximate, sample from, and compare distributions of distances…
We prove that the limit profile of star transpositions at time $t= n \log n +cn$ is equal to $d_{\text{T.V.}}(\text{Poiss}(1+e^{-c}), \text{Poiss}(1))$. We prove this by developing a technique for comparing the limit profile behavior of two…
We introduce a powerful scan statistic and the corresponding test for detecting the presence and pinpointing the location of a change point within the distribution of a data sequence with the data elements residing in a separable metric…
We propose a model of card shuffling where a pack of cards, spread as points on a square table, are repeatedly gathered locally at random spots and then spread towards a random direction. A shuffling of the cards is then obtained by…
Particle simulations confined by sharp walls usually develop an oscillatory density profile. For some applications, most notably soft matter liquids, this behavior is often unrealistic and one expects a monotonic density climb instead. To…
We prove that the limit profile of a sequence of reversible Markov chains exhibiting total variation cutoff is a continuous function, under a computable condition involving the spectrum of the transition matrix and the cutoff window.
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
In this paper, we investigate the mixing time of the adjacent transposition shuffle for a deck of $N$ cards. We prove that around time $N^2\log N/(2\pi^2)$, the total variation distance to equilibrium of the deck distribution drops abruptly…
Recent work in differential privacy has highlighted the shuffled model as a promising avenue to compute accurate statistics while keeping raw data in users' hands. We present a protocol in this model that estimates histograms with error…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and…
This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from a linear regime to a sublinear regime at time $n/2$. Here,…
In this paper we study the mixing time of a biased transpositions shuffle on a set of $N$ cards with $N/2$ cards of two types. For a parameter $0<a \le 1$, one type of card is chosen to transpose with a bias of $\frac{a}{N}$ and the other…