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Results tagged with probabilistic-method
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user 36721
Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.
3
votes
Accepted
Probabilistic method Alon and Spencer Azuma's inequality
$\newcommand\ep\epsilon$The martingale $(X_i)$ is given by the formula
$$X_i:=E(X|\ep_1,\dots\ep_i).$$
By the independence of the $\ep_i$'s,
$$X_i=g_i(\ep_1,\dots,\ep_i),$$
where
$$g_i(t_1,\dots,t_i): …
- 128k
12
votes
Accepted
Theorems like the Lovász Local Lemma?
A large number of results for sums $W$ of possibly dependent indicators of events (that is, for sums of possibly dependent Bernoulli random variables) $X_i$ have been obtained by the Chen--Stein metho …
- 128k