Weighted cogrowth formula for free groups (Q784885)
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scientific article; zbMATH DE number 7227230
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weighted cogrowth formula for free groups |
scientific article; zbMATH DE number 7227230 |
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Weighted cogrowth formula for free groups (English)
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3 August 2020
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Summary: We investigate the relationship between geometric, analytic and probabilistic indices for quotients of the Cayley graph of the free group \(\text{Cay}(F_n)\) by an arbitrary subgroup \(G\) of \(F_n\). Our main result, which generalizes Grigorchuk's cogrowth formula to variable edge lengths, provides a formula relating the bottom of the spectrum of weighted Laplacian on \(G \backslash \text{Cay}(F_n)\) to the Poincaré exponent of \(G\). Our main tool is the Patterson-Sullivan theory for Cayley graphs with variable edge lengths.
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Cayley graph of free group
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cogrowth
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discrete Laplacian
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bottom of spectrum
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spectral radius
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Green function
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Patterson-Sullivan theory
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