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math.GR2025
Linear-growth harmonic functions for nonsymmetric random walks on groups of polynomial growth
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
Let be a finitely generated group of polynomial growth and let be an adapted, Abelian-centered probability measure with a finite exponential moment (not necessarily symmetr…
math.GR2025
Exact versus monotone isoperimetric profiles of finitely generated groups
Mayukh Mukherjee
Gromov asked whether the exact isoperimetric profile of an infinite finitely generated group is comparable, at the same cardinality, to its greatest nondecreasing minorant. We comp…