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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.
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Combinatorics for a stochastic dynamics problem
Suppose we have a circular arrangement (periodic boundaries) with $M$ sites and we want to distribute $N$ particles over these sites such that there are occupation numbers $n_m$ that respect $\sum_m n …
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Taylor approximation of a function of a random variable
Suppose we have a random variable $X$ and a smooth function $g$. We want to calculate the expectation value $\mathbb{E}(g(X))$. To be able to write down at least an approximate solution, we perform a …