Related papers: Strong approximation for the supermarket model

Given the first 20-100 coefficients of a typical generating function of the type that arises in many problems of statistical mechanics or enumerative combinatorics, we show that the method of differential approximants performs surprisingly…

Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…

We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…

We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the…

We consider a revenue-maximizing seller with $n$ items facing a single buyer. We introduce the notion of symmetric menu complexity of a mechanism, which counts the number of distinct options the buyer may purchase, up to permutations of the…

We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

Customers arrive at rate N times alpha on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate beta. We let N go to infinity.We prove a functional…

Consider a monopolist selling $n$ items to an additive buyer whose item values are drawn from independent distributions $F_1,F_2,\ldots,F_n$ possibly having unbounded support. Unlike in the single-item case, it is well known that the…

Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…

In this work we are concerned with the design of efficient mechanisms while eliciting limited information from the agents. First, we study the performance of sampling approximations in facility location games. Our key result is to show that…

High-tech systems are typically produced in two stages: 1) Production of components using specialized equipment and staff; 2) System assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of…

We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…

We consider N single server infinite buffer queues with service rate beta. Customers arrive at rate N times alpha,choose L queues uniformly, and join the shortest one. The stability condition is alpha strictly less than beta. We study in…

When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…

We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…

Serfozo (2009, Theorem 2.65) gives a useful central limit theorem for processes with regenerative increments. Unfortunately, there is a gap in the proof. We fill this gap, and at the same time we weaken the assumptions. Furthermore, we give…

One of the core applications of machine learning to knowledge discovery consists on building a function (a hypothesis) from a given amount of data (for instance a decision tree or a neural network) such that we can use it afterwards to…