Related papers: Multiple drawing multi-colour urns by stochastic a…
A cyclic urn is an urn model for balls of types $0,\ldots,m-1$ where in each draw the ball drawn, say of type $j$, is returned to the urn together with a new ball of type $j+1 \mod m$. The case $m=2$ is the well-known Friedman urn. The…
For the interacting urn model with polynomial reinforcement, it has been conjectured that almost surely one color monopolizes all the urns if the interaction parameter $p>0$. We disprove the conjecture. For the case $p=1$, we give a…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
In this work we present a simple and efficient algorithm which, with high probability, provides an almost uniform sample from the set of proper k-colourings on an instance of a sparse random graph G(n,d/n), where k=k(d) is a sufficiently…
A cyclic urn is an urn model for balls of types $0,\ldots,m-1$. The urn starts at time zero with an initial configuration. Then, in each time step, first a ball is drawn from the urn uniformly and independently from the past. If its type is…
This paper deals with a new design methodology for stratified comparative experiments based on interacting reinforced urn systems. The key idea is to model the interaction between urns for borrowing information across strata and to use it…
We propose a way of finding a Stein type characterization of a given absolutely continuous distribution $\mu$ on $\R$ which is motivated by a regression property satisfied by an exchangeable pair $(W,W')$ where $\calL(W)$ is supposed or…
This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…
This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966),…
In a recent paper, the authors studied the distribution properties of a class of exchangeable processes, called measure-valued P\'{o}lya sequences (MVPS), which arise as the observation process in a generalized urn sampling scheme. Here we…
We explain the relation between certain random tiling models and interacting particle systems belonging to the anisotropic KPZ (Kardar-Parisi-Zhang) universality class in 2+1-dimensions. The link between these two \emph{a priori} disjoint…
We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that…
I present a generalization of the Ehrenfest urn model that is aimed at simulating the approach to equilibrium in a dilute gas. The present model differs from the original one in two respects: 1) the two boxes have different volumes and are…
The paper concerns the classical occupancy scheme with infinitely many boxes. We establish approximations to the distributions of the number of occupied boxes, and of the number of boxes containing exactly r balls, within the family of…
The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer science. In its simplest form, the planted…
Consider a bin containing $n$ balls colored with two colors. In a $k$-query, $k$ balls are selected by a questioner and the oracle's reply is related (depending on the computation model being considered) to the distribution of colors of the…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
The purpose of this note is to draw attention to problems related to a concept called majority colouring recently studied by Kreutzer, Oum, Seymour, van der Zypen and Wood. They raised a problem of determining, for a natural number $k$, the…
We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…
We survey the design of elections that are resilient to attempted interference by third parties. For example, suppose votes have been cast in an election between two candidates, and then each vote is randomly changed with a small…