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Results tagged with pr.probability
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user 152785
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
5
votes
1
answer
112
views
Does there exist a constant $C$, such that, $\Pr[\max_k|\sum_{i\neq k}X_i|\ge t]\le C\Pr[|\s...
Let $X_1, \ldots, X_n$ be independent symmetric variables. Now I would like to know whether there exists a constant $C$, such that
$$
\Pr[\max_{k \in [n]} |\sum_{i \in [n] \setminus \{k\}} X_i| \ge …
- 175
2
votes
Hypercontractivity of two simple random variables, $E[XY]^s \le E[X^s]E[Y^s].$
Define $q_1 = p_{11} + p_{12}$ and $q_2 = p_{11} + p_{21}$ and set
$$
f(1) = \sqrt[s]{\frac{\frac{1}{2} + x}{q_1}}
$$
$$
f(-1) = \sqrt[s]{\frac{\frac{1}{2} - x}{1 - q_1}}
$$
$$
g(1) = \sqr …
- 175