Cesaro mean distribution of group automata starting from measures with summable decay

Consider a finite Abelian group (G,+), with |G|=p^r, p a prime number, and F: G^N -> G^N the cellular automaton given by {F(x)}_n= A x_n + B x_{n+1} for any n in N, where A and B are integers relatively primes to p. We prove that if P is a translation invariant probability measure on G^Z determining a chain with complete connections and summable decay of correlations, then for any w= (w_i:i<0) the Cesaro mean distribution of the time iterates of the automaton with initial distribution P_w --the law P conditioned to w on the left of the origin-- converges to the uniform product measure on G^N. The proof uses a regeneration representation of P

Stationary processes whose filtrations are standard

We study the standard property of the natural filtration associated to a 0--1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.Comment: Published at http://dx.doi.org/10.1214/009117906000000151 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamical behaviour of Coven's aperiodic cellular automata

AbstractWe show that the aperiodic cellular automata studied by Coven (1980), that is the maps F : [0, 1]Z → [0, 1]Z induced by block maps f : [0, 1]r + 1 → [0, 1] such that f(x0,x1,…,xr) is equal to (x0 + 1)mod 2 if x1…xr = b1…br and equal to x0 otherwise, where B = b1…br is a given aperiodic word, have the following position in classification of K…rka (1994): they are regular, contain equicontinuous points without being equicontinuous, and are chain transitive but not topologically transitive. Therefore they do not have the shadowing property; this answers in the negative a question raised by P. K…rka

The social costs of sounding gay: voice-based impressions of adoption applicants

In three studies (total N = 239) we examined the unexplored question of whether voice conveying sexual orientation elicits stigma and discrimination in the context of adoption. Studies 1 and 2 were conducted in Italy where same-sex adoption is illegal and controversial. Study 3 was conducted in the United Kingdom where same-sex adoption is legal and generally more accepted. The three studies show that listeners draw strong inferences from voice when judging hypothetical adoption seekers. Both Italian and British listeners judged gay-sounding speakers as warmer and as having better parenting skills, yet Italian participants consistently preferred straight over gay-sounding applicants, whereas British participants showed an opposite tendency, presumably reflecting the different normative context in the two countries. We conclude that vocal cues may have culturally distinct effects on judgment and decision making and that people with gay-sounding voices may face discrimination in adoption procedures in countries with antigay norms.info:eu-repo/semantics/acceptedVersio