Embree-Trefethen constant

In mathematics, the Embree-Trefethen constant is a threshold value in number theory labelled β*.

For

0 < β < β* = 0.70258 approximately,

solutions to the random recurrence

x_n+1=x_n±βx_n-1

decay exponentially as n→∞ with probability one, whereas for

β > β*

they grow exponentially.

Seen another way, if σ(β) is the rate of exponential growth or decay of the random recurrance for given β, then

σ(1)=1.13198824 approximately

is Viswanath's constant, while

σ(β*)=1

for the Embree-Trefethen constant.