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www.jeremykun.com | ||
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francisbach.com
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djalil.chafai.net
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| | | | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | |
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thenumb.at
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lucatrevisan.wordpress.com
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| | | Today we will see how to use the analysis of the multiplicative weights algorithm in order to construct pseudorandom sets. The method will yield constructions that are optimal in terms of the size of the pseudorandom set, but not very efficient, although there is at least one case (getting an ``almost pairwise independent'' pseudorandom generator)... | ||
