## Volume and time doubling of graphs and random walks: The strongly recurrent case.(English)Zbl 1021.60037

The author proves upper and lower off-diagonal, sub-Gaussian transition probability estimates for strongly recurrent random walks under necessary and sufficient conditions. Besides the known conditions, volume doubling and the elliptic Harnack inequality, a new property of time doubling is introduced. If $$E(x,R)$$ is the expected time until exit from the ball of radius $$R$$ centred at $$x$$ for a random walk starting from $$x$$, this property requires that $$E(x,2R)\leq D_E E(x,R)$$ for a constant $$D_E>0$$.

### MSC:

 60G50 Sums of independent random variables; random walks 31C20 Discrete potential theory 35K05 Heat equation 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)

### Keywords:

random walk on graph; doubling property; Harnack inequality
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### References:

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