Displaying similar documents to “Random walks with k -wise independent increments.”

Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables

Hiroyuki Okazaki, Yasunari Shidama (2010)

Formalized Mathematics

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In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and real-valued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev's inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this article we define the algebra of real-valued random variables.

Upper tails of self-intersection local times of random walks: survey of proof techniques

Wolfgang König (2010)

Actes des rencontres du CIRM

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The asymptotics of the probability that the self-intersection local time of a random walk on d exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some...