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quomodocumque.wordpress.com | ||
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almostsuremath.com
The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... |
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www.ethanepperly.com
[AI summary] A detailed mathematical blog post explaining how spectral theory and eigenvalues provide quantitative proofs for the convergence and mixing time of reversible Markov chains. |
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qchu.wordpress.com
In this post we'll describe the representation theory of theadditive group scheme$latex \mathbb{G}_a$ over a field $latex k$. The answer turns out to depend dramatically on whether or not $latex k$ has characteristic zero. Preliminaries over an arbitrary ring (All rings and algebras are commutative unless otherwise stated.) The additive group scheme $latex \mathbb{G}_a$ over... |
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francisbach.com
[AI summary] This mathematical post explores the geometry of positive semi-definite matrices using the von Neumann entropy and related Bregman divergences to derive concentration inequalities for random matrices. |
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