21-3 Joe Neeman, Charles Radin, Lorenzo Sadun

MODERATE DEVIATIONS IN TRIANGLE COUNT (555K, pdf) Jan 23, 21

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Abstract. We prove moderate deviations bounds for the number of triangles in a G(n,m) random graph, complementing recent results of Goldschmidt et al. The moderate deviations of triangle density in G(n,m) graphs change qualitatively between the regime of the central limit theorem and the regime of large deviations, with those of Goldschmidt et al. extending the former and our results extending the latter; we also conjecture a precise form of sharp change between the regimes. Our results can be interpreted as finite size effects in phase transitions in constrained edge-triangle graphs.

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