Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz Functions on Expanders are Typically Flat   This work studies the typical behavior of random integer-valued Lipschitz
functions on expander graphs with sufficiently good expansion. We consider two
families of functions: M-Lipschitz functions (functions that change by at most
M along edges) and integer-homomorphisms (functions that change by exactly 1
along edges). We prove that such functions typically exhibit very small
fluctuations. For instance, we show that a uniformly chosen M-Lipschitz
function takes only M+1 values on most of the graph, with a double exponential
decay for the probability to take other values.

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The categories of this paper are: alg-geom
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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int