# Tagged Questions

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### GOE convergence

As is well-known (at least in some circles), eigenvalue spacing distribution for large symmetric matrices converges as size goes to infinity (see this question for more background). The question is: ...
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### Stationary point processes with arbitrarily slow decorrelation

A point process $P$ (a probability measure on simple, locally finite point configurations $\mathcal{C}$ on $\mathbb{R}$ - I'm restricting to the one-dimensional setting) is stationary when ...
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### Minimum of Random Energy Model (REM) with logarithmically correlated potential

In the paper [FB] (ArXiv, J. Phys. A), the authors analyse a particular Random Energy Model (REM) with logarithmically correlated potential and conjecture in Eq. (2) that the distribution function of ...
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### First return time in an interval for N particles rotating on the circle at constant random speeds

Here is my problem: draw N velocities $v_1,v_2,\dots,v_n$ in $[-\pi,\pi]^N$ from some measure (Haar measure of uniform independent for simplicity) and make $N$ particles rotate around the circle with ...
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### How to evaluate the wiener measure of sets?

I would like to understand how the Wiener measure of some simple sets can be evaluated. I will sketch the construction of Wiener measure I have in mind: We denote the one point compactification of ...
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### Free Boson Correlator $\langle X(z)X(w) \rangle =- \ln |z - w|$

In physics papers, the massless free boson has a definition involving an action: $$S(X) = \frac{1}{8\pi} \int d\sigma^2\, \partial X \overline{\partial X}$$ The random functions $X(z)$ are ...
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### References for a physicist migrating to stochastic processes

I've studied "Markov Chains" - Norris and "Measure, Integral and Probability" - Capinski, Kopp. Now, I'm looking for a couple of books (or other references) that help me bridging these two topics. ...
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### Diffusion equation on mixing of diffusing particles

I am trying to study mixing of diffusing particles like it was done by E. Ben-Naim On the Mixing of Diﬀusing Particles. The picture below shows the idea how permutations and inversion numbers reflect ...
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### $\{\phi:\int \phi d\mu=0\}$ for a fixed shift invariant $\mu$

Given a shift invariant probability measure $\mu$ on a mixing subshift of finite type. What are the Lipschitz functions with zero integral with respect to the measure $\mu?$ Clearly any ...
I am working on a certain collision problem. The probability of forming $j$ particles upon collision of $m$ and $n$ particles is given by the following equation: ...