Formulas are discussed for the asymptotic growth rate of summands in tensor powers in monoidal categories with infinitely many indecomposables, using generalized Perron-Frobenius theory and random walk techniques.
Growth problems in diagram categories
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abstract
In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
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math.CT 1years
2024 1verdicts
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Asymptotics in infinite monoidal categories
Formulas are discussed for the asymptotic growth rate of summands in tensor powers in monoidal categories with infinitely many indecomposables, using generalized Perron-Frobenius theory and random walk techniques.