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12 papers · 1 filter
Hyperbolicity and stable polynomials in combinatorics and probability
Robin Pemantle
This was the basis of two lectures in the Current Developments in Mathematics conference in 2011. These lectures survey the theory of hyperbolic and stable polynomials, from their…
Sampling 3-colourings of regular bipartite graphs
David Galvin
We show that if $\gS=(V,E)$ is a regular bipartite graph for which the expansion of subsets of a single parity of is reasonably good and which satisfies a certain local conditi…
On the least singular value of random symmetric matrices
Hoi H. Nguyen
Let be an by symmetric matrix whose entries are bounded by for some . Consider a randomly perturbed matrix , where is a random symmetric…
Sharp Thresholds for Monotone Non Boolean Functions and Social Choice Theory
Gil Kalai, Elchanan Mossel
A key fact in the theory of Boolean functions is that they often undergo sharp thresholds. For example: if the function is m…
A Littlewood-Richardson rule for Macdonald polynomials
Martha Yip
Macdonald polynomials are orthogonal polynomials associated to root systems, and in the type A case, the symmetric kind is a common generalization of Schur functions, Macdonald sph…
Profiles of permutations
Michael Lugo
This paper develops an analogy between the cycle structure of, on the one hand, random permutations with cycle lengths restricted to lie in an infinite set with asymptotic dens…