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Results tagged with pr.probability
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user 9850
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
21
votes
3
answers
2k
views
what is the cycle length of the maximum normalized cycle in the directed complete graph?
Consider the complete, directed graph on $n$ vertices. Let the edge lengths $\{X_{ij}: 1 \leq i, j \leq n\}$ be i.i.d standard normal, with the constraint $X_{ij} = -X_{ji}$. The value of a normalized …
- 1,010
1
vote
Sparse representation of a distribution with independent and correlated variables
As I answer I'm rephrasing and clarifying your question a little - please correct me if something is wrong.
Firstly, shouldn't your equation have an extra term of the form $\Delta(x,y)$ on the RHS, …
- 1,010
51
votes
0
answers
2k
views
Alternating colors on a line: infinitely often or converge?
Suppose we have intervals of alternating color on $\mathbb{R}$ (say, red / blue / red / blue / …). All intervals have independent length, with all red intervals distributed as $\mathbb{P}_{R}$, all b …
- 1,010
0
votes
Lower bound for Gaussian random vector with negative correlation
Thanks Didier. The last line you wrote gave me an idea, and I think I managed to get a sharp bound for the i.i.d exp(1) case.
(A minor correction: $X_i = (Y_i - Y_{i+1})/\sqrt{2}$, not $/2$)
Usin …
- 1,010
5
votes
3
answers
886
views
Lower bound for Gaussian random vector with negative correlation
Let $X = (X_1,\ldots,X_n) \in \mathbb{R}^n$ be jointly Gaussian with mean $0$, covariance matrix: $Var(X_i) = 1$, $Cov(X_i, X_{i+1}) = -1/2$, and $Cov(X_i, X_j) = 0$ else.
Let $\zeta \in \mathbb{R}^ …
- 1,010