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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, June 30, 2022}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{room 106, building 28}

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{\large\scshape Maksim Zhukovskii 
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  (Weizmann Institute)
}
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will talk about
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{\Large\bfseries Extremal independence in discrete random systems\par}
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\textsc{Abstract:}
Let G be a graph with several vertices v\_1,..,v\_r being roots. A G-extension of u\_1,..,u\_r in a graph H is a subgraph G* of H such that there exists a bijection from V(G) to V(G*) that maps v\_i to u\_i and preserves edges of G with at least one non-root vertex. It is well known that, in dense binomial random graphs, the maximum number of G-extensions obeys the law of large numbers. The talk is devoted to new results describing the limit distribution of the maximum number of G-extensions. To prove these results, we develop new bounds on the probability that none of a given finite set of events occur. Our inequalities allow us to distinguish between weakly and strongly dependent events in contrast to well-known Janson's and Suen's inequalities as well as Lovasz Local Lemma. These bounds imply a general result on the convergence of maxima of dependent random variables.





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{\bfseries Please Note the Unusual Place!}
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