11 citations · 35 across the 21 of their papers we have counts for
7 papers · 1 filter
The Jacobi Theta Distribution
Caleb Deen Bastian, Grzegorz Rempala, Herschel Rabitz
We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the p…
Individual molecules dynamics in reaction network models
Daniele Cappelletti, Grzegorz A. Rempala
In a stochastic reaction network setting we consider the problem of tracking the fate of individual molecules. We show that using the classical large volume limit results, we may a…
Orthogonal Dice
Caleb Deen Bastian, Herschel Rabitz, Grzegorz A Rempala
In this paper, we introduce a family of discrete rectangular uniform distributions on the natural numbers-referred to as orthogonal dice-characterized by the property that their me…
Throwing Stones and Collecting Bones: Looking for Poisson-like Random Measures
Caleb Deen Bastian, Grzegorz A. Rempala
We show that in a broad class of random counting measures one may identify only three that are rescaled versions of themselves when restricted to a subspace. These are Poisson, bin…
Functional Central Limit Theorem For Susceptible-Infected Process On Configuration Model Graphs
Wasiur R. KhudaBukhsh, Casper Woroszylo, Grzegorz A. Rempała +1
We study a stochastic compartmental susceptible-infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval $[…
Double asymptotics for the chi-square statistic
Grzegorz A. Rempała, Jacek Wesołowski
We consider distributional limit of the Pearson chi-square statistic when the number of classes m increases with the sample size n in such way that . Under mild m…