Search Results

Here $\alpha$ is a number, and $H$ is a measure. I believe that you should take a finite space, say, $\{1,...,K\}$. Then for any partition of $\{1,...,K\}$, your first formula will hold. $H$ measure …

You should probably look at the Girsanov's theorem http://en.wikipedia.org/wiki/Girsanov_theorem The process $X$ is a probability distrubution on the space of continuous functions, so is the Wiener p …

You may think of the conditional expectation as follows: $\mathbb{E}(X|\mathcal{F})$ for a r.v. $X$ is the average value of $X$ based on our knowledge of "information" that is given by the sigma-algeb …

Take $N$ independent walkers on the one-dimensional lattice $\mathbb{Z}$ (i.e., independent random walks, biased or not). Condition that these walkers do not collide till the end of time. Then the con …

The $S$-matrix you write can be written as $\frac{x_\alpha-Q x_\beta}{x_\alpha-x_\beta}$, where $x_{\alpha,\beta}^{}$ are some fractional linear transformations of $\xi_{\alpha,\beta}^{}$, and $Q$ is …

Let $X_1,\ldots ,X_N$ be independent identically distributed random variables (or, more generally, exchangeable random variables, but let's assume independence for simplicity). Then $$ E(X_i\mid X_1+ …

To expand on my comments, this paper https://arxiv.org/pdf/hep-th/9209083v2.pdf by Shatashvili deals with ``correlation functions'' of Haar unitary matrices of the form $$ \int_{U(N)}^{} d\mu(U) e_{}^ …

I am interested in finding a monotone coupling between two random variables. Let $\alpha_1>\alpha_2$, $b<a$. Define the following two (non-normalized) densities on the whole real line: \begin{align*} …

This is not a complete answer, but more of an approach and an invitation to look at the relevant literature. As you write, you would like to insert the so-called Fermi factor into the Fredholm Pfaffia …

I'm trying to set straight various $q$-deformations of the standard geometric distribution. The geometric distribution on $\left\{ 0,1,\ldots \right\}$ is well-known, it has $$ \mu_1(X=j)=(1-p)p^j,\q …