# 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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### Given multiple posets, what is the probability that a randomly selected (uniform dist) subposet of their product has a max under the product order?

Given multiple totally ordered posets, how do I find the probability that a randomly selected (with uniform distribution) subposet of their product has a maximum under the product order? I have some ...
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### Reference request - random regular graphs vs random graphs w/ degree sequence

There are some properties that are easily studied for random d-regular graphs, but that are very hard to extend to random graphs with a given degree sequence (e.g. whether a graph is w.h.p. ...
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### Dislocations and Random Matrix Theory

Does anyone have a good reference book that works as a good starting point for an analyst to learn about the connection between Random Matrix Theory and Dislocations? Thank you for your help. By ...
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### Hitting Time-Analogue for Chaotic Systems

Let a topologically mixing dynamical map $f$ on $\mathbb{R}^n$, and define the dynamical system with initial value $x \in \mathbb{R}^n$ by $$x_{t+1}^x = f(x_t^x),\, x_0^x=x .$$ Fix $y\in\mathbb{R}^n$...
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### Distributions associated with random sets and sums of random sets

Let's say you have an infinite random set $S$ of non-negative integers, and $T=S+S=\{x+y$ with $x,y\in S\}$. Let $N_S(z)$ be the number of elements of $S$ less than or equal to $z$; it is a random ...
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### Random walk in a switching scenery

For each $x \in \mathbf{Z}$ let $(\eta_t(x))_{t\geq0}$ denote independent copies of a process $(\eta_t(0))_{t\geq0}$ defined as follows. The process $\eta_t(0)$ takes values in $\{-1,1\}$, where $-1$ ...
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### Exit time for Brownian motion with stochastic barriers

I am interested in the expected exit time of a one-dimensional Brownian particle from a stochastically evolving interval as follows. Context: If $L_t$ and $R_t$ denote the distance to the left and ...
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### English translation of “Une inégalité pour martingales à indices multiples et ses applications”

Does anyone know of a English translation of "Une inégalité pour martingales à indices multiples et ses applications" by Renzo Cairoli. Or could translate the statement of the martingale ...
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### How to calculate possible arrangements of hexagons?

I was wondering someone could help. I've developed a board game which is made up of six, large hexagonal board pieces, which can be arranged in any order, and with any rotation/arrangement of sides ...
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### On the difference between Malliavin derivative and Gross-Sobolev derivative

Let $W=C_0([0,1],\mathbb R^d)$ be the classical Wiener space equipped with $\mu$ the Wiener measure. If $F:W\to\mathbb R$ is a cylindrical function of the form \begin{align*} F(w)=f(W_{t_1}(w),\cdots,...
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### How do you know that you have succeeded-Constructive Quantum Field Theory and Lagrangian

Quantum Field Theory is a branch of mathematical physics which is begging for a better understanding. In fact there are no rigorous constructions of interacting QFT in four dimensions. By a rigorous ...
Suppose that $X_i\sim X$ and $Y_j\sim Y$ are independent samples of heavy-tailed random variables (with the same power-law tail index $\alpha$ but possibly differing tail prefactors), such that the ...
I am not familiar with random matrices but I need to confirm the correctness of the inequality below. Let $\xi_i\in\{\pm 1\}$ be independent random signs, and let $A_1,\ldots, A_n$ be $m\times m$ ...