Tye Lidman

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math.PR2007

Asymptotic evolution of acyclic random mappings

Steven N. Evans, Tye Lidman

An acyclic mapping from an $n$ element set into itself is a mapping $ϕ$ such that if $ϕ^{k} (x) = x$ for some $k$ and $x$ , then $ϕ (x) = x$ . Equivalently, $ϕ^{ℓ} = ϕ^{ℓ + 1} = ...$ f…

math.PR2006

Expectation, Conditional Expectation and Martingales in Local Fields

Steven N. Evans, Tye Lidman

We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$ -adic numbers. We define the expect…