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Results tagged with pr.probability
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user 83189
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
8
votes
0
answers
303
views
Maximum probability of a set of vectors from $ \mathbb{F}_2^n $ being linearly independent
Suppose $ m $ vectors from the vector space $ \mathbb{F}_2^n $ are selected independently according to a distribution $ P $ over $ \mathbb{F}_2^n $. Here $ \mathbb{F}_2 $ denotes the field with two el …
- 503
3
votes
1
answer
201
views
Bound on an integral representing a difference of two relative entropies
Let $ f : [0,1] \to \mathbb{R} $ be a function satisfying: 1.) $ |f(x)| \leqslant a $ for some $ a < 1 $, and 2.) $ \int_0^1 f(x) {\mathrm d}x = 0 $. I would like to know whether the following inequal …
- 503
1
vote
1
answer
132
views
Does a random matrix over $\mathbb{Z}_q$ map linearly independent vectors to statistically i...
Suppose $A \in \mathbb{Z}_q^{n \times m}$ is a random $n \times m$ matrix whose entries are i.i.d. uniform over $\mathbb{Z}_q=\mathbb{Z}/q\mathbb{Z}$, where $q\geq2$. Let $\mathbf{x}_1, \ldots, \mathb …
- 503