Related papers: Sampling Part Sizes of Random Integer Partitions
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of…
We derive an asymptotic formula for $A(n,j,r)$ the number of integer partitions of $n$ into at most $j$ parts each part $\le r$. We assume $j$ and $r$ are near their mean values. We also investigate the second largest part, the number of…
This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size $m$. In particular, the size of the sample is allowed to be…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
In this work we study the set size distribution estimation problem, where elements are randomly sampled from a collection of non-overlapping sets and we seek to recover the original set size distribution from the samples. This problem has…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
Let $(X_1,X_2,...)$ be a random partition of the unit interval $[0,1]$, i.e. $X_i\geq0$ and $\sum_{i\geq1} X_i=1$, and let $(\varepsilon_1,\varepsilon_2,...)$ be i.i.d. Bernoulli random variables of parameter $p \in (0,1)$. The Bernoulli…
The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a finite partition. We study the asymptotic behavior of the raking-ratio empirical process…
Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become…
This paper studies the \emph{subset sampling} problem. The input is a set $\mathcal{S}$ of $n$ records together with a function $\textbf{p}$ that assigns each record $v\in\mathcal{S}$ a probability $\textbf{p}(v)$. A query returns a random…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
Many big-data clusters store data in large partitions that support access at a coarse, partition-level granularity. As a result, approximate query processing via row-level sampling is inefficient, often requiring reads of many partitions.…
We use the Circle Method to derive asymptotic formulas for functions related to the number of parts of partitions in particular residue classes.
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
We study partitions of totally positive integers in real quadratic fields. We develop an algorithm for computing the number of partitions, prove a result about the parity of the partition function, and characterize the quadratic fields such…
A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning…