# 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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### The probability that iid draws from a mean zero random variable sum to zero

Suppose we have a probability distribution $p(\cdot)$ supported on the integers between $-m$ and $m$ for some positive integer $m$, with $\sum_k kp(k) = 0$. Suppose furthermore that all $p(k)$ are ...
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### Hopf monads in categorical probability theory

1. Context. According to [1], probability monads are arguably the most important concept in categorical probability theory. In [2] Fritz and Perrone argue that "in order for a monad to really ...
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### Lower bounds for truncated moments of Gaussian measures on Hilbert space

Let $\mu_C$ be a centered Gaussian probability Borel measure on a real separable Hilbert space $\mathcal{H}$ with covariance operator $C$. Denote the ball with radius $r$ in $\mathcal{H}$ centered at ...
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### The fluctuations of a random path

Suppose I have a $n \times n$ square grid and for each square, I assign 1 with probability $\frac{1}{2}$ and 0 with probability $\frac{1}{2}$. On the boundary, I put 1s on the lower half and 0s on the ...
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### Reference request: Gaussian measures on duals of nuclear spaces

I am interested in constructive quantum field theory where Gaussian measures on duals of nuclear spaces (specifically, the space of tempered distribution $\mathcal{S}'(\mathbb{R}^n)$) play a key role. ...
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### Dimension-free sample complexity for the inverse of Gaussian sample covariance?

Suppose I have $m$ samples drawn from a Gaussian in $\mathbb{R}^n$, and need the inverse of the sample covariance $\Sigma_m^{-1}$ to be $\varepsilon$-close to true inverse covariance $\Sigma^{-1}$ (in ...
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### Weak limit of pushforward measures with finite second moments is also a pushforward measure with finite second moment

Suppose $\mu \in P(\mathbb{R}^d)$ and for each $n$, $T_n:\mathbb{R^d} \rightarrow \mathbb{R^d}$ is such that the pushforward $T_n \# \mu$ has a finite second moment. If $\{T_n \# \mu\}$ converges ...
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