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quomodocumque.wordpress.com
| | qchu.wordpress.com
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| | 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...
| | www.ethanepperly.com
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| | [AI summary] The provided text is a detailed mathematical exploration of Markov chains, focusing on their convergence properties, the role of reversibility in ensuring convergence to a stationary distribution, and the analysis of total variation distance and chi-squared divergence as measures of convergence. It also includes derivations of bounds on the mixing time of Markov chains and the application of spectral properties of the transition matrix to analyze convergence rates.
| | lucatrevisan.wordpress.com
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| | The spectral norm of the infinite $latex {d}&fg=000000$-regular tree is $latex {2 \sqrt {d-1}}&fg=000000$. We will see what this means and how to prove it. When talking about the expansion of random graphs, abobut the construction of Ramanujan expanders, as well as about sparsifiers, community detection, and several other problems, the number $latex {2 \sqrt{d-1}}&fg=000000$...
| | thekittymaths.wordpress.com
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| A Compendium of Cool Internet Math Things