Geodesic
Synchronizing random automata on $4$-letter alphabet
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IV, Tome 402 (2012), pp. 83-90

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The paper deals with the synchronization of a random automaton that is sampled uniformly at random from the set of all automata with $n$ states and $m$ letters. We show that for $m=4$ the probability that a random automaton is synchronizing is larger than a positive constant. 
@article{ZNSL_2012_402_a5,
     author = {Yu. I. Zaks and E. S. Skvortsov},
     title = {Synchronizing random automata on $4$-letter alphabet},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {83--90},
     publisher = {mathdoc},
     volume = {402},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_402_a5/}
}
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Yu. I. Zaks; E. S. Skvortsov. Synchronizing random automata on $4$-letter alphabet. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IV, Tome 402 (2012), pp. 83-90. http://geodesic.mathdoc.fr/item/ZNSL_2012_402_a5/