# Tagged Questions

Use this tag only if your question is about the modern theoretical footing for probability, for example probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use [tag:probability-...

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### (Infinite hat)-guessing problem

$2$ men are playing a game: they are wearing countably infinitely many hats on their heads. The hats are either black or white with probability $\frac 12$. They see the other's man hats but cannot see ...
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### Lipschitz constant/derivative of the stationary distribution of a Markov chain under perturbations in the transition kernel

I'm interested in the following question: Given a parameter $t\in \mathbb{R}$ and a column stochastic matrix $P(t)$ (i.e., $e^T P(t)=e^T$ and $P(t)_{ij}\ge 0$), calculate the Lipschitz constant of ...
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### Is statistical physics background desirable for probability theory?

I am talking about higher probability viz. Brownian Motion, Ergodic Theory, Concentration, Percolation, Random Graphs, Random Matrix, etc. Going through books, I find that somehow or the other, many ...
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### What is the “time change” of an adapted finite-variation stochastic process?

Let $(\Omega, \mathcal F,\mathbb P)$ be a probability space equipped with a filtration $\{\mathcal F_t:t\in\mathbb R_+\}$ satisfying the usual conditions of completeness and right-continuity. Suppose ...
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### Stopping-time sigma-algebra and the case at infinity, definition question.

Assume you have a probability space $(\Omega,\mathcal{F},P)$, and you have a filtration $\{\mathcal{F}_t\}$ and a stopping time $\tau$. Then all the books I have seen define the stopping time sigma-...
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