Ehud Friedgut

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Consider a function f : f0;1g n ! f0;1g. The sensitivity of a point v 2 f0;1g n is jfv 0 : f (v 0) 6 = f (v); dist(v; v 0) = 1gj, i.e. the number of neighbors of the point in the discrete cube on which the value of f diiers. The average sensitivity of f is the average of the sensitivity of all points in f0;1g n. (This can also be interpreted as the sum of(More)
Let f k (n; p) denote the probability that the random graph G(n; p) is k-colorable. We show that for every k 3, there exists d k (n) such that for any > 0, lim n!1 f k (n; d k (n) ? n) = 1 and lim n!1 f k (n; d k (n) + n) = 0 : As a result we conclude that for any given value of n the the chromatic number of G(n; d=n) is concentrated in one value for all(More)
Let σ ∈ Sk and τ ∈ Sn be permutations. We say τ contains σ if there exist 1 ≤ x1 < x2 < . . . < xk ≤ n such that τ(xi) < τ(xj) if and only if σ(i) < σ(j). If τ does not contain σ we say τ avoids σ. Let F (n, σ) = |{τ ∈ Sn| τ avoids σ}|. Stanley and Wilf conjectured that for any σ ∈ Sk there exists a constant c = c(σ) such that F (n, σ) ≤ cn for all n. Here(More)
The Gibbard-Satterthwaite theorem states that every non-trivial voting method among at least 3 alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with non-negligible probability for every neutral voting method among 3 alternatives(More)
We consider powers of regular graphs defined by the weak graph product and give a characterization of maximum-size independent sets for a wide family of base graphs which includes, among others, complete graphs, line graphs of regular graphs which contain a perfect matching and Kneser graphs. In many cases this also characterizes the optimal colorings of(More)