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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

3 votes

2d moment of chebyshev

If you are interested in approximation for large $n,d$, with a simple Poissonization argument I get: $$ E(X^{2d}) \approx n^{2d} \left( \frac{1+e^{-2\lambda}}{2} \right)^n$$ where $\lambda = \frac{ …
leonbloy's user avatar
  • 318
3 votes
0 answers
136 views

Random assignment problem under multinomial or Poisson distribution

We place $m$ balls at random (uniformly) inside $n^2$ urns arranged as a $n \times n$ square. Then we must choose $n$ urns, such that no two urns belong to the same row or column, with the objective o …
leonbloy's user avatar
  • 318
3 votes

Probability of a Random Walk crossing a straight line

(Just a hint. Should be a comment more than an answer, but don't have enough rep) It seems interesting the slightly more general problem in which the initial distance to the line is greater than zero …
leonbloy's user avatar
  • 318