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www.randomservices.org | ||
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terrytao.wordpress.com
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| | | | | In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory, as well as setting up basic probabilistic notation that we... | |
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troll-audio.com
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| | | | | A frequent claim by detractors of digital audio is that the time resolution is equal to the sampling interval, 22.7 ?s for the CD format. This is incorrect. Although there is a limit, it is much sm... | |
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djalil.chafai.net
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| | | | | This tiny post is adapted from the introduction of a recent work with David García-Zelada and Paul Jungon the macroscopics and edge of a planar jellium seen as a Coulomb gas. Potential theory.The Coulomb kernel $g$ in $\mathbb{R}^d$, $d\geq1$, is given for all $x\in\mathbb{R}^d$ by \[ g(x)=\begin{cases}\displaystyle\log\frac{1}{|x|}&\text{if $d=2$}\\[1em]\displaystyle\frac{1}{(d-2)|x|^{d-2}}&\text{if $d\neq2$}\end{cases}.\] The Coulomb... | |
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almostsuremath.com
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| | | In the previous post I started by introducing the concept of a stochastic process, and their modifications. It is necessary to introduce a further concept, to represent the information available at each time. A filtration $latex {\{\mathcal{F}_t\}_{t\ge 0}}&fg=000000$ on a probability space $latex {(\Omega,\mathcal{F},{\mathbb P})}&fg=000000$ is a collection of sub-sigma-algebras of $latex {\mathcal{F}}&fg=000000$ satisfying $latex... | ||
