Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diameters of random Cayley graphs of finite nilpotent groups   We prove the existence of a limiting distribution for the appropriately
rescaled diameters of random undirected Cayley graphs of finite nilpotent
groups of bounded rank and nilpotency class, thus extending a result of Shapira
and Zuck which dealt with the case of abelian groups. The limiting distribution
is defined on a space of unimodular lattices, as in the case of random Cayley
graphs of abelian groups. Our result, when specialised to a certain family of
unitriangular groups, establishes a very recent conjecture of Hermon and
Thomas. We derive this as a consequence of a general inequality, showing that
the diameter of a Cayley graph of a nilpotent group is governed by the diameter
of its abelianisation.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th