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almostsuremath.com | ||
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xorshammer.com
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| | | | | Nonstandard Analysis is usually used to introduce infinitesimals into the real numbers in an attempt to make arguments in analysis more intuitive. The idea is that you construct a superset $latex \mathbb{R}^*$ which contains the reals and also some infinitesimals, prove that some statement holds of $latex \mathbb{R}^*$, and then use a general "transfer principle"... | |
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jmanton.wordpress.com
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| | | | | If $latex Y$ is a $latex \sigma(X)$-measurable random variable then there exists a Borel-measurable function $latex f \colon \mathbb{R} \rightarrow \mathbb{R}$ such that $latex Y = f(X)$. The standard proof of this fact leaves several questions unanswered. This note explains what goes wrong when attempting a "direct" proof. It also explains how the standard proof... | |
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djalil.chafai.net
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| | | | | The logarithmic potential is a classical object of potential theory intimately connected with the two dimensional Laplacian. It appears also in free probability theory via the free entropy, and in partial differential equations e.g. Patlak-Keller-Segel models. This post concerns only it usage for the spectra of non Hermitian random matrices. Let \( {\mathcal{P}(\mathbb{C})} \) be the set of probability measures... | |
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rhubbarb.wordpress.com
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| | | My previous post was written with the help of a few very useful tools: LaTeX mathematical typesetting Gummi LaTeX editor Python programming language PyX Python / LaTeX graphics package my own PyPyX wrapper around PyX LaTeX2WP script for easy conversion from LaTeX to WordPress HTML | ||
