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Measures on $\mathbb Q_p$

Because $\mathbb Q_p$ is a locally compact abelian group it has a natural translation invariant measure, Haar measure, which allows us to formulate a natural theory of integration of (certain) real valued functions over subsets… Read More »Measures on $\mathbb Q_p$

The Canonical Ensemble

The canonical ensemble is a probability space which models physical systems at a fixed temperature, but for which the energy can vary. In this situation we imagine that our system, described by states $(\Omega, \mathcal… Read More »The Canonical Ensemble

$p$-adic Electrostatics

An introduction to non-archimedean electrostatics in the context of $\mathbb Z_p$.

Background

See The $p$-adics and Related Concepts for notation and basics on the $p$-adic numbers, Introduction to Boltzmann Statistics for notation and background on electrostatics, and Basics of Probability for notation and background on probability and… Read More »Background