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Random 0-1 rectangular matrices: a probabilistic analysis

Periodica Mathematica Hungarica
Authors:
Guy Louchard
and
Helmut Prodinger

Abstract

Carlitz considered in [5]
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$r \times n$$ \end{document}
matrices with entries being zero or one and the number of changes, i.e., the number of (horizontally or vertically) adjacent entries which are different. We extend these results in many ways. For instance, we exhibit that the limiting distribution is Gaussian and get explicit formul for some moments even in the general instance of d dimensions (instead of just two).
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Number of survivors in the presence of a demon

Periodica Mathematica Hungarica
Authors:
Guy Louchard
,
Helmut Prodinger
, and
Mark Ward

Abstract

This paper complements the analysis of Louchard and Prodinger [LP08] on the number of rounds in a coin-flipping selection algorithm that occurs in the presence of a demon. We precisely analyze a very different aspect of the selection algorithm, using different methods of analysis. Specifically, we obtain precise descriptions of the distribution and all moments of the number of participants ultimately selected during the execution of the algorithm. The selection algorithm is robust in at least two significant ways. The presence of a demon allows for the precise analysis even when errors may occur between the rounds of the selection process. (The analysis also handles the more traditional case, in which no demon is involved.) The selection algorithm can also use either biased or unbiased coins.

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