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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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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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| | | | | The martingale property is strong enough to ensure that, under relatively weak conditions, we are guaranteed convergence of the processes as time goes to infinity. In a previous post, I used Doob's upcrossing inequality to show that, with probability one, discrete-time martingales will converge at infinity under the extra condition of $latex {L^1}&fg=000000$-boundedness. Here, I... | |
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www.robertkubinec.com
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| | | Ordered beta regression can give you comparable, scale-free ATEs that can still be understood in the scale of the original data-all without using logs. | ||
