Almost all trees have quantum symmetry
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DOI: 10.1007/s00013-020-01476-x
Abstract: From the work of Erdős and Rényi from 1963, it is known that almost all graphs have no symmetry. In 2017, Lupini, Mančinska, and Roberson proved a quantum counterpart: Almost all graphs have no quantum… read more here.
Keywords: almost trees; trees quantum; quantum symmetry; symmetry ... See more keywords
A generalization of the Erdös–Rényi limit theorem and the corresponding multifractal analysis
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DOI: 10.1016/j.jnt.2018.04.019
Abstract: Abstract Let m ≥ 2 and 1 ≤ p ≤ m − 1 be two integers. Denote by Σ ¯ p ⊂ { 0 , 1 , … , m − 1 } the alphabet… read more here.
Keywords: erd nyi; generalization erd; limit theorem; limit ... See more keywords
The probability of unusually large components in the near-critical Erdős–Rényi graph
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DOI: 10.1017/apr.2018.12
Abstract: Abstract The largest components of the critical Erdős–Rényi graph, G(n, p) with p = 1 / n, have size of order n 2/3 with high probability. We give detailed asymptotics for the probability that there… read more here.
Keywords: probability; critical erd; erd nyi; unusually large ... See more keywords
Prevalence of deficiency-zero reaction networks in an Erdös–Rényi framework
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DOI: 10.1017/jpr.2021.65
Abstract: Reaction networks are commonly used within the mathematical biology and mathematical chemistry communities to model the dynamics of interacting species. These models differ from the typical graphs found in random graph theory since their vertices… read more here.
Keywords: erd nyi; reaction networks; reaction; networks erd ... See more keywords
Moderate deviations of subgraph counts in the Erdős-Rényi random graphs 𝐺(𝑛,𝑚) and 𝐺(𝑛,𝑝)
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DOI: 10.1090/tran/8117
Abstract: The main contribution of this article is an asymptotic expression for the rate associated with moderate deviations of subgraph counts in the Erdős-Rényi random graph G ( n , m ) G(n,m) . Our approach… read more here.
Keywords: subgraph counts; erd nyi; moderate deviations; nyi random ... See more keywords