Giulia Cencetti — Università di Firenze #
Non-transitive games: from coin tossing to walkers on graphs #
In a random sequence of heads or tails, with a fair coin, every subsequence appears evenly. However, given 
a sequence, there is always another one that appears first, statistically. Betting on subsequences is a 
non-transitive game, like rock-paper-scissors. The analysis of non-transitivity can be extended to any 
Markov process, and also used for analysing real data. We found that there is a phase transition in the 
degree of non-transitivity for unfair coins, and that in general this degree depends on certain properties 
of the Markov process, in particular we analyzed diffusion processes on graphs. We finally started 
applying this concept to the analysis of DNA sequences.
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In collaboration with F. Bagnoli and D. Fanelli