Related papers: New results on a generalized coupon collector prob…
Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Pek\"oz, R\"ollin, and Ross (2016, arXiv:1309.4183 [math.PR]) exploited characterizing distributional fixed…
In this note we give a proof for the result stated as Theorem 4 in Poisson Approximation in a Poisson Limit Theorem Inspired by Coupon Collecting.
Universal compression algorithms have been studied in the past for sequential change detection, where they have been used to estimate the post-change distribution in the modified version of the Cumulative Sum (CUSUM) Test. In this paper, we…
We address a well-known problem in combinatorics involving the identification of counterfeit coins with a systematic approach. The methodology can be applied to cases where the total number of coins is exceedingly large such that brute…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably…
We survey recent results concerning the total-variation mixing time of the simple exclusion process on the segment (symmetric and asymmetric) and a continuum analog, the simple random walk on the simplex with an emphasis on cutoff results.…
The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…
This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at…
An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling…
We consider Markov decision processes (MDP) as generators of sequences of probability distributions over states. A probability distribution is p-synchronizing if the probability mass is at least p in a single state, or in a given set of…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
We study the poor-biased model for money exchange introduced in [2]: agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random.…
Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when…
Coding over subsets (known as generations) rather than over all content blocks in P2P distribution networks and other applications is necessary for a number of practical reasons such as computational complexity. A penalty for coding only…
We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and,…
Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a…
The generalised random graph contains $n$ vertices with positive i.i.d. weights. The probability of adding an edge between two vertices is increasing in their weights. We require the weight distribution to have finite second moments and…
We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means,…