On Sloane's persistence problem
Time and place
1 PM on Thursday, September 19th, 2013; NAC 6/113
Edson De Faria (University of Sao Paulo)
Abstract
We investigate the so-called persistence problem of Sloane,
exploiting connections with the dynamics of circle maps and the
ergodic theory of $\mathbb{Z}^d$ actions.
We also formulate a conjecture, concerning the asymptotic
distribution of digits in long products of primes chosen from a
given finite set, whose truth would in particular solve the
persistence problem. We provide computational evidence and an
heuristic argument in favor of our conjecture. Such heuristics can
be thought in terms of a simple model in statistical mechanics.
This talk is based on joint work with Charles Tresser (IBM).
