Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances

From Extreme Values of I.I.D. Random Fields to Extreme Eigenvalues of Finite-volume Anderson Hamiltonian

The aim of this paper is to study asymptotic geometric properties almost surely or/and in probability of extreme order statistics of an i.i.d. random field (potential) indexed by sites of multidimensional lattice cube, the volume of which unboundedly increases. We discuss the following topics: (I) high level exceedances, in particular, clustering of exceedances; (II) decay rate of spacings in comparison with increasing rate of extreme order statistics; (III) minimum of spacings of successive order statistics; (IV) asymptotic behavior of values neighboring to extremes and so on. The conditions …

关于超模函数和亚模函数在超立方体上的塔拉甘型相关不等式

Talagrand-Type Correlation Inequalities for Submodular and Supermodular Functions on the Hypercube

本文研究了在超立方体上亚模和超模函数的相关不等式，证明了在特定条件下协方差的下界，并验证了Friedgut-Kahn-Kalai-Keller谱猜想。