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4 votes
1 answer
346 views

Mehta integral and orthogonality

The Mehta integral is the following expression: $$\frac{1}{(2\pi)^{n/2}}\int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} \prod_{i=1}^n e^{-t_i^2/2} \prod_{1 \le i < j \le n} |t_i - t_j |^{2 \...
12 votes
3 answers
3k views

Infinitesimal generators of stochastic processes

What's the $L^1$ analogue of Stone's theorem saying that any strongly continuous 1-parameter unitary groups has a unique self-adjoint generator? More precisely: let $X$ be a measure space ($\sigma$-...