We show how to recover Euler's formula for $\zeta(2n)$, as well as $L_{\chi_4}(2n+1)$, for any integer $n$, from the knowledge of the density of the product $\mathbb{C}_1,\mathbb{C}_2\ldots,\mathbb{C}_k$, for any $k\geq 1$, where the $\mathbb{C}_i$'s are independent standard Cauchy variables.

Consider the random walk $S_n=\xi_1+\cdots+\xi_n$ with independent and identically distributed increments and negative mean $\mathbf E\xi=-m<0$. Let $M=\sup_{0\le i} S_i$ be the supremum of the random walk.  In this note we present derivation of asymptotics for $\mathbf P(M>x), x\to\infty$ for…

We consider the random walk attachment graph introduced by Saramäki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge.  We show that if the length of the random…