The Probabilistic Method

By B. Bollobás. Fundamentals of Ramsey Theory, 2015

1,130 citations recorded by the source corpus.

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Subfields: Biomedical Engineering, Computational Mechanics, Numerical Analysis

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Citations in the corpus

Sparse pseudo-random graphs are Hamiltonian (2003, neutral): “Essentially all of them are easy corollaries of the following well-known result whose proof can be found, inter alia, in Chapter 9 of a monograph of Alon and Spencer [4].”
A Probabilistic Technique for Finding Almost-Periods of Convolutions (2010, neutral): “Let N be a positive integer and suppose that f : [N ] → [0, 1] is a function with average Ex∈[N ]f(x) = α.”
Minima in branching random walks (2007, positive): “ ≥ 1} = Ω(1/n5/2) = Ω(1/m5/2). To prove Fact 7, we use a version of the second moment method often called the Chung-Erdo˝s inequality (see Chung and Erd¨os (1952) and also Devroye and Reed (1995) and Alon and Spencer (2000), Chapter 2), which in our setting can be stated as follows: for any integer ”
EIGENVALUES AND LINEAR QUASIRANDOM HYPERGRAPHS (2012, neutral): “For background on graph expansion and eigenvalues, see [1, 5, 26].”
The Repulsive Lattice Gas, the Independent-Set Polynomial, and the Lovász Local Lemma (2003, neutral): “Erdős and Spencer [40] (see also [2, 83]) later noted that the same conclusion holds even if Ax and σ(Ay: y ∈ X \ Γ∗(x)) are not independent, provided that the “harmful” conditional probabilities are suitably bounded.”
Secure multiparty computation of approximations (2001, neutral): “where (1) follows from a version of the Cherno bound (e.g., see [ 5 ]).”
Approximation of the Stability Number of a Graph via Copositive Programming (2002, neutral): “148 of [1]).”
Sieving by large integers and covering systems of congruences (2005, neutral): “This result bears a resemblance to the Lovász Local Lemma (for example, see [1]), and may be stronger than it in some situations.”