Deviation Inequalities And Moderate Deviations On The Number Of Isolated Vertices In Sparse Random Graphs

Let V(n, p) denote the number of isolated vertices in G(n, p), where p=c/n, c > 0 . In this paper we study the deviation inequality and the moderate deviation principle of V(n,p). First, using Chebyschev inequality we get a deviation inequality of V(n,p). Second, as an application of the deviation inequality, we get Marcinkiewicz-Zygmund strong law of large numbers. Finally, using Stirling formula and Gartner-Ellis theorem, we get the moderate , deviation principle of V(n,p).