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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
4
votes
3
answers
704
views
Measure of intersections in probability spaces
Let $(X,\mu)$ be a probability space, and $0<\epsilon<1/2$. Let $\{A_i:i\in \mathbb{N}\}$ be a collection of measurable subsets of $X$ such that $\mu(A_i)\geq \epsilon$ for all $i\in\mathbb{N}$.
Is i …
9
votes
1
answer
562
views
combinatorics on cyclic sequences
Given $m\geq 1$, let $I=(a_1,\ldots,a_{3m})$ be a sequence such that $I$ contains exactly $m$ zeros, $m$ ones, and $m$ twos.
Given $i=1,2$ and $j\leq 3m,k\leq m$ we can define $$U_{i,j}(k)=\text{numb …