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Results tagged with large-deviations
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user 106377
5
votes
4
answers
384
views
Concentration of closed random walks
Consider a random walk $S_n=\sum_{i=1}^n X_i$ where $P(X_i=+1)=P(X_i=-1)=1/2$ with $n$ large. By Chernoff's bound we know that, for example, $\sum_{i=1}^{n/2} X_i=O(\sqrt{n})$ with high probability.
…
- 470
2
votes
Accepted
Concentration of closed random walks
I believe the following coupling argument shows that (in particular) if we specify that the random walk ends at 0 then halfway through the walk the probability that we're within distance $\lambda$ of …
- 470