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Results tagged with pr.probability
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user 21690
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
2
answers
381
views
Distribution of the area statistic for Catalan paths
A Catalan path of semilength $n$ is a path from $(0,0)$ to $(2n,0)$ that proceeds by taking northeast (1,1) or southeast (1,-1) steps, and never goes below the $x$-axis. The area of a path $P$ is the …
- 1,112
10
votes
Accepted
A game of plates and olives
The answer to Question 1 is that yes, the belief is justified. By Stirling's approximation, $(2n+1)!!=n^n(2/e)^{n(1+o(1))}$ or $\log (2n+1)!! = n \log n +n(2/e)(1+o(1))$, so for an affirmative answer …
- 1,112