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Embree-trefethen ConstantIn mathematics, the Embree-Trefethen constant is a threshold value in number theory labelled β*. For a fixed real β, consider the recurrence - xn+1=xn±βxn-1
where the sign in the sum is chosen at random for each n independently with equal probabilities for "+" and "-". In can be proven that for any choice of β, the limit -
exists almost surely. In informal words, the sequence behaves exponentially with probability one—and σ(β) can be interpreted as its almost sure rate of exponential growth. For - 0 < β < β* = 0.70258 approximately,
solutions to this recurrence decay exponentially as n→∞ with probability one, whereas for - β > β*
they grow exponentially. Regarding values of σ, we have: External link
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