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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.

4 votes

Chances to win an election

You question about balls is still not well-defined. You would be able to solve it if you had some a priori probability on the set of possible distributions of preferences of voters. Then you data woul …
Ilya Nikokoshev's user avatar
1 vote

Homology of algebraic varieties in Okounkov's paper on enumerating algebraic curves

It appears that you want the "rough, introductory answers", so feel fine to ask more detailed questions if anything is unclear/potentially wrong. Also, I only have very general knowledge about enumera …
Ilya Nikokoshev's user avatar
11 votes
Accepted

"The" random tree

I learned about The random graph a week ago from the blog post on n-cafe (thanks to Andrew and sdcvvc for the links!). Your construction, while slightly different, can be examined in the same way as …
Ilya Nikokoshev's user avatar
12 votes

If you break a stick at two points chosen uniformly, the probability the three resulting sti...

Yes, here's a nice and beautiful argument! First you should draw a picture of axes a and b. You're asked to select uniformly a point in the square [0,1]x[0,1]. Now because of the symmetry (sic!) it's …
Ilya Nikokoshev's user avatar
9 votes
6 answers
3k views

Primes are pseudorandom?

I've been reading the wonderful slides by Terry Tao and thought about this question. Primes appear to be quite random, and the formal statement should be that there are some characteristics of primes …
Ilya Nikokoshev's user avatar