# Tag Info

## New answers tagged pr.probability

### About Palm distribution

C. Palm's theory of spatial point processes relies heavily on measure theory in an abstract setting. A more gentle introduction is given in the lecture notes Conditioning in spatial point processes. ...
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### Quadratic variation of supremum of brownian motion

The quadratic variation is identically $0$, i.e. $$\langle S, S \rangle_t = 0$$ for all $t$, almost surely. To see this, note that $S$ is almost surely increasing, hence has bounded variation almost ...
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### Concentration inequality for the spectral norm of the product of normalized Gaussian (and subgaussian) matrices in high dimensions

Vershynin, R. Spectral norm of products of random and deterministic matrices. Probab. Theory Relat. Fields 150, 471–509 (2011). This result is a sharp bound on the spectral norm of $W=BA$, where $A$ ...

### Concentration inequality for the spectral norm of the product of normalized Gaussian (and subgaussian) matrices in high dimensions

The Marcenko-Pastur resut (see, e.g., https://www.sciencedirect.com/science/article/pii/S0047259X85710512) gives you the Stieljes equation of the limiting spectral distributions of matrices of the ...
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### Comparing diffusion processes in different metrics

The generator of the diffusion corresponding to a Riemannian metric (i.e., the diffusion process which the limit of the random walks such that their increments go along geodesics and the ...
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### A question related to the CDFs of multivariate normal distribution

The joint cdf of a multivariate distribution uniquely determines the distribution. So, if the cdf's of multivariate normal distributions are the same, then their mean vectors must be the same (and ...

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### Sum of a Poisson point process

The density function of $Z$ is the Dickman $\rho$ function, normalized (that is, divided by its mass, $e^{\gamma}$). This function, $\rho\colon [0,\infty)\to (0,\infty)$, is defined via $\rho(t)=1$ ...
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There is a formula for the Laplace transform of any additive functional of a Poisson process with intensity measure $\lambda$. Specifically, for any non-negative measurable function $f$, E\left[e^{-\...