A large-deviations principle for all the components in a sparse inhomogeneous random graph
A large-deviations principle for all the components in a sparse inhomogeneous random graph
Abstract We study an inhomogeneous sparse random graph, $${\mathcal G }_N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> , on $$[N]=\{1,\dots ,N\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>N</mml:mi> <mml:mo>]</mml:mo> <mml:mo>=</mml:mo> <mml:mo>{</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> as introduced in a seminal paper by Bollobás et al. (Random Struct …