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Приглашаем Ваc на доклад Михаила Шишкина, младшего научного сотрудника Международной лаборатории статистической и вычислительной геномики, который расскажет о работе "Large Deviation Results in Population Genetics" (https://www.jstor.org/stable/2244397).

Abstract: Let {Xn} be a Markov chain on a bounded set in Rd with Ex(X1) = fN(x) = x + βN hN(x), where x0 is a stable fixed point of fN(x) = x, and $\operatorname{Cov}_x(X_1) \approx \sigma^2(x)/N$ in various senses. Let D be an open set containing x0, and assume hN(x) → h(x) uniformly in D and either $\beta_N \equiv 1$ or $\beta_N \rightarrow 0, \beta_N \gg \sqrt{\log N/N}$. Then, assuming various regularity conditions and X0 ∈ D, the time the process takes to exit from D is logarithmically equivalent in probability to eVNβN, where $V > 0$ is the solution of a variational problem of Freidlin-Wentzell type $\lbrack \text{if} \beta_N \rightarrow 0 \text{and} d = 1, V = \inf\{2 \int^y_{x_0}\sigma^{-2}(u)|h(u) du|: y \in \partial D\} \rbrack$. These results apply to the Wright-Fisher model in population genetics, where {Xn} represent gene frequencies and the average effect of forces such as selection and mutation are much stronger than effects due to finite population size.

Ссылка на видеовстречу: https://telemost.yandex.ru/j/53039387975230