Which values of the volume growth and escape time exponent are possible for a graph

104 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Stability of parabolic Harnack inequalities (2003, background): “2. Explicit examples of graphs satisfying these conditions, for various 2, are given in [ B1 ], [BB2], and [Jo].”
The Alexander-Orbach conjecture holds in high dimensions (2008, background): “In fact, we now know that any value of β between 2 and df + 1 may appear [6].”
Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs (2005, background): “Following [4], we say that a graph is very strongly recurrent if there exists p1 F 0 such that, writing TA 9 min K n J 0 : Xn 7 A O , Ty 9 T y , τ C x 6 r D 9 TB r x ` r s c , (1.”
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, background): “e walk dimension, even though it is, strictly speaking, not a dimension of a geometric object. It is possible to prove that if the metric space (X;d) satises a chain condition, then 2 dW dH+1, see [14,37,39]. When dW = 2, one speaks of Gaussian estimates and when dW >2, one speaks then of sub-Gau”