慶應義塾大学 理工学部 数理科学科

タイトル Two applications of probability in analysis
開催日時 2018年10月19日 17:00-18:00
主催者
講演者 Rahul Roy氏 (Indian Statistical Institute)
場所 慶應義塾大学 矢上キャンパス
14棟631A/B
内容 Ever since Kakutani showed that the Dirichlet problem is intricately connected with the Brownian motion, many questions of analysis have been solved by probabilistic methods. In this talk we discuss two such questions. In the first part we discuss the Poisson equation $\frac{1}{2} \bigtriangleup u = -1 \mbox{ on a domain } D \subset \mathbb R^d$ with boundary conditions $u = 0 \mbox{ on } \delta D.$ We obtain an explicit solution for this problem when $D$ is an equilateral triangle. Next we provide a probabilistic proof of the Euler's formula $\zeta(2) = \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$, where $\zeta$ is the Riemann's zeta function.
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