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math.PR2024★ 1 cited
Bond percolation does not simulate site percolation
Nikita Gladkov, Aleksandr Zimin
We show that a site percolation is a stronger model than a bond percolation. We use the van den Berg -- Kesten (vdBK) inequality to prove that site percolation on a neighborhood of…
math.PR2020
On existence of measure with given marginals supported on a hyperplane
Alexander P. Zimin
Let be absolutely continuous probability measures on the real line such that every measure is supported on the segment and the density functi…
math.PR2018★ 5 cited
Dependency-dependent Bounds for Sums of Dependent Random Variables
Christoph H. Lampert, Liva Ralaivola, Alexander Zimin
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific de…