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The largest square of successes covering the origin for Bernoulli trials on the lattice
Author(s) -
Kopociński B.
Publication year - 1995
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1995.tb01453.x
Subject(s) - square lattice , mathematics , bernoulli's principle , integer lattice , bernoulli trial , bernoulli distribution , lattice (music) , combinatorics , poisson distribution , random variable , square (algebra) , statistical physics , discrete mathematics , statistics , geometry , physics , condensed matter physics , acoustics , ising model , thermodynamics , half integer
Consider a collection of Bernoulli random variables on the two dimensional integer lattice and define the length D of the side of the largest square consisting entirely of successes, which covers the origin of the lattice. The paper gives a method to evaluate the probability distribution function of D . An analogous problem for the Poisson process on the plane is also considered.