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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.

11 votes
4 answers
3k views

What is the cover time of a random walk on a cube?

I can't quite figure this problem yet. There is an ant at one vertex of a cube. The ant goes from one vertex to another by choosing one of the neighboring vertices uniformly at random. What is the ave …
zzzbbx's user avatar
  • 241
11 votes
1 answer
434 views

(almost) statistical independence of nodes degrees in a graph

Wireless networks are typically modeled as random geometric graphs. The number of nodes $N$ in the network is drawn from a Poisson distribution with intensity $\lambda$ $$P(N = n) = \frac{\lambda^n …
zzzbbx's user avatar
  • 241
8 votes
8 answers
5k views

probability and math puzzle books/references [closed]

Hi All, I'd like to solve some math puzzles, especially in the context of probability theory, but I'm open to other areas too. The kind of problems that does not require much knowledge of mathematics, …
2 votes
1 answer
452 views

metric for signal to noise ratio in communication systems

I'm not quite sure about how to define a good measure of the quality of a communication channel with fading and interference. Let us assume the simplest case, where a node in a network receives the fo …
zzzbbx's user avatar
  • 241