Lisa Hofer
Published 2017-04-03Version 1
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem, we use the method of dependency graphs. The main difficulty is then to estimate the variance of our statistics. We need a lower bound on the variance, for which we introduce a recursive technique based on the law of total variance.
Central limit theorems for Gaussian polytopes
A Central Limit Theorem for Repeating Patterns
A central limit theorem for descents and major indices in fixed conjugacy classes of $S_n$
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