The Pascal adic transformation is loosely Bernoulli
Zero Krengel entropy does not kill Poisson entropy
We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann–Kakutani odometer), but whose associated Poisson suspension has positive entropy.
Almost-sure growth rate of generalized random Fibonacci sequences
We study the generalized random Fibonacci sequences defined by their first non-negative terms and for ≥1, +2= +1± (linear case) and +2=| +1± | (non-linear case), where each ± sign is independent and either + with probability or − with probability 1− (0<≤1). Our main result is that, when is of the form =2cos(/) for some integer ≥3, the exponential growth of for 0<≤1,...
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