Non-Amenable Cayley Graphs Of High Girth Have PC
-
Asaf Nachmias
,
-
Yuval Peres
Electronic Communications in Probability
|
, Vol 17
In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., p_c < p_u. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical exponents. In particular, the self-avoiding walk has positive speed.
- Asaf Nachmias ,
- Yuval Peres
Electronic Communications in Probability | , Vol 17
In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., p_c < p_u. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical exponents. In particular, the self-avoiding walk has positive speed.