# Questions tagged [pr.probability]

Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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### What's the minimum ratio of positive cells such that the player has a positive probability to reach the boundary of a large random map?

A map with $(2n-1)$ rows and $(2n-1)$ columns of square cells is generated randomly as follows: the value of each cell is chosen from {1, -1} randomly and independently with probability {$p$, $1-p$}. ...
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### Finding the limit of a specific sequence of linear processes

Given a strictly stationary random process $(\xi_t)_{t \in \mathbb Z}$. Define $\mu:= E[\xi_t]$, for all $t$. Suppose $(\xi_t)_{t \in \mathbb Z}$ ergodic: \begin{equation}\label{a}\tag{E} \frac{1}{n}\...
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### Scheduling "parent talks" at school

Real life motivation. In my younger son's class, there are $18$ students. His teacher provided $18$ time slots for the parents of each child to have a 30-minute conversation of their kid's progress in ...
I wonder whether a $d$-dimensional random walk $S_n$, generated by the infinite i.i.d. copies of X given by: $X=e_1=(1, 0, 0, ..., 0)$ (with probability $p_1$) $X=e_2=(0, 1, 0, ..., 0)$ (with ...