All Questions

Let $d$ be a large positive integer and fix $r \ge 0$. Set $S := B_2^n \cap [-r,r]^d$, where $B_2^d$ is the euclidean unit-ball in $\mathbb R^d$. Finally, let $\omega(S)$ be the Gaussian width of $S$, ...

Let $(W_t)_{t\geq0}$ be a standard Brownian motion in $\mathbb{R}^n$ and $(A_t)_{t\geq0}$ be an adapted matrix-valued process such that $A_t$ is a positive symmetric matrix with bounded operator norm :...

Introducing the notion of a random measure, textbooks usually start with a locally compact second countable Hausdorff space. Where does this requirement come from? I would like to have a motivation ...

Consider a Markov chain on a state-space which is slightly weird: It is the space of all tilings of a hexagon as shown in the left-hand side of the figure below with three types of rhombi: yellow, ...

The question Average Value of Area Closed by Brownian Motion turned out to be about the Lévy area process, which measures "signed area with multiplicity" enclosed by Brownian motion (e.g. each ...