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Results tagged with pr.probability
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user 93775
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
10
votes
3
answers
2k
views
Random Walks on high dimensional spaces
I've read on a paper that, in the two dimensional case, if you start from the origin and take steps of length one in arbitrary directions (uniformely on the unit sphere $S^1$, not left-right-up-down), …
- 899
1
vote
1
answer
237
views
Probability of two Points being divided by an high-Dimensional Hyperplane
I have two points $x_1,x_2 \in \mathbb S^n $ which are distant $d$ from each other, where $d<<1$.
I also have a vector $v$ sampled uniformly at random from $\mathbb S^n$.
What is the probability that …
- 899
1
vote
1
answer
168
views
Expected norm of linear maps
I want to compute the expected norm of a vector-matrix multiplication. I have a vector $x \in \mathbb{R}^n$ with norm one and a matrix $M \in \mathbb{R}^{n \times n}$, whose entries are iid taken from …
- 899
5
votes
1
answer
3k
views
Eigenvalues and eigenvectors of Gaussian random matrices
Let us assume we have a square matrix $A$ whose entries are sampled from a standard Gaussian distribution of mean $0$. Do we have any information about the distribution of its eigenvalues?
Particula …
- 899