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YCor
YCor
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Diameter of component graph of Uniformuniform spanning forests on the amenable transitive graph with super polynomial growth

According to the paper Benjamini, Kesten, Peres, and Schramm - Geometry of the Uniform Spanning Forestuniform spanning forest: Transitionstransitions in Dimensionsdimensions 4, 8, 12 (Annals, we have that2004), the diameter of the component graph of the USFuniform spanning forests (USF) on $d$-dimensional transitive graph is $\lfloor(d-1)/4\rfloor$. 

I wonder if the diameter of the component graph of the USF on the amenable transitive graph with superpolynomal growth is infinite. Actually, I think the answer is yes for every transitive graph with superpolynomial growth. A concrete example is that I think the component graph of WUSF on 3-regular tree has infinite diameter. But 3-regular tree is not amenable.

Diameter of component graph of Uniform spanning forests on the amenable transitive graph with super polynomial growth

According to the paper Benjamini, Kesten, Peres, and Schramm - Geometry of the Uniform Spanning Forest: Transitions in Dimensions 4, 8, 12, we have that the diameter of the component graph of the USF on $d$-dimensional transitive graph is $\lfloor(d-1)/4\rfloor$. I wonder if the diameter of the component graph of the USF on the amenable transitive graph with superpolynomal growth is infinite. Actually, I think the answer is yes for every transitive graph with superpolynomial growth. A concrete example is that I think the component graph of WUSF on 3-regular tree has infinite diameter. But 3-regular tree is not amenable.

Diameter of component graph of uniform spanning forests on the amenable transitive graph with super polynomial growth

According to the paper Benjamini, Kesten, Peres, and Schramm - Geometry of the uniform spanning forest: transitions in dimensions 4, 8, 12 (Annals, 2004), the diameter of the component graph of the uniform spanning forests (USF) on $d$-dimensional transitive graph is $\lfloor(d-1)/4\rfloor$. 

I wonder if the diameter of the component graph of the USF on the amenable transitive graph with superpolynomal growth is infinite. Actually, I think the answer is yes for every transitive graph with superpolynomial growth. A concrete example is that I think the component graph of WUSF on 3-regular tree has infinite diameter. But 3-regular tree is not amenable.

Name of paper; typo
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LSpice
LSpice
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diameter Diameter of component graph of Uniform spanning forests on the amenable transitive graph with super polynomial growth

accordingAccording to the paper httpsBenjamini, Kesten, Peres, and Schramm - Geometry of the Uniform Spanning Forest://arxiv.org/abs/math/0107140 Transitions in Dimensions 4, 8, 12, we have known that the diameter of the component graph of the USF on d$d$-dimensional transitive graph is $[n-1]/4$,$\lfloor(d-1)/4\rfloor$. I wonder if the diameter of the component graph of the USF on the amenable transitive graph with superpolynoimalsuperpolynomal growth is infinite. Actually, I think the answer is yes for every transitive graph with superpolynomial growth. A concrete example is that I think the component graph of WUSF on 3-regular tree has infinite diameter. But 3-regular tree is not amenable.

diameter of component graph of Uniform spanning forests on the amenable transitive graph with super polynomial growth

according to the paper https://arxiv.org/abs/math/0107140, we have known that the diameter of the component graph of the USF on d-dimensional transitive graph is $[n-1]/4$, I wonder if the diameter of the component graph of the USF on the amenable transitive graph with superpolynoimal growth is infinite. Actually, I think the answer is yes for every transitive graph with superpolynomial growth. A concrete example is that I think the component graph of WUSF on 3-regular tree has infinite diameter. But 3-regular tree is not amenable.

Diameter of component graph of Uniform spanning forests on the amenable transitive graph with super polynomial growth

According to the paper Benjamini, Kesten, Peres, and Schramm - Geometry of the Uniform Spanning Forest: Transitions in Dimensions 4, 8, 12, we have that the diameter of the component graph of the USF on $d$-dimensional transitive graph is $\lfloor(d-1)/4\rfloor$. I wonder if the diameter of the component graph of the USF on the amenable transitive graph with superpolynomal growth is infinite. Actually, I think the answer is yes for every transitive graph with superpolynomial growth. A concrete example is that I think the component graph of WUSF on 3-regular tree has infinite diameter. But 3-regular tree is not amenable.

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none Yuan
none Yuan
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diameter of component graph of Uniform spanning forests on the amenable transitive graph with super polynomial growth

according to the paper https://arxiv.org/abs/math/0107140, we have known that the diameter of the component graph of the USF on d-dimensional transitive graph is $[n-1]/4$, I wonder if the diameter of the component graph of the USF on the amenable transitive graph with superpolynoimal growth is infinite. Actually, I think the answer is yes for every transitive graph with superpolynomial growth. A concrete example is that I think the component graph of WUSF on 3-regular tree has infinite diameter. But 3-regular tree is not amenable.