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Game saturation of intersecting families

Balázs Patkós, Máté Vizer (2014)

Open Mathematics

We consider the following combinatorial game: two players, Fast and Slow, claim k-element subsets of [n] = 1, 2, …, n alternately, one at each turn, so that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed k-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone...

Geometric influences II: Correlation inequalities and noise sensitivity

Nathan Keller, Elchanan Mossel, Arnab Sen (2014)

Annales de l'I.H.P. Probabilités et statistiques

In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand’s lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini–Kalai–Schramm (BKS) noise sensitivity theorem....

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