5 problems

Let $a$ be odd, and let the initial state $z$ be either $\frac{a-1}{2}$ or $\frac{a+1}{2}$, each with probability $\frac{1}{2}$. Consider the gambler's ruin game in which the gambl…

Consider a gambler's ruin process on the integer interval from $0$ to $N$, with absorption at the endpoints. From an interior position $x$, the particle moves to $x-1$ with probabi…

Conjectured limiting-probability claim. Each probability in $T$ converges to the corresponding entry of $M$ as $N$ grows.

Let the gambler's ruin process evolve on $\mathbb{E}=\{0,\ldots,N\}$, with birth probabilities $p(i)$ and death probabilities $q(i)$, and let $W_{0:i:N}$ denote its duration condit…

Consider a nearest-neighbor open quantum random walk on the vertices $\{0,\dots,M\}$ induced by matrices $L$ and $R$ satisfying … For an initial internal density matrix $\rho$, let…