Joint large deviation result for empirical measures of the coloured random geometric graphs
نویسندگان
چکیده
منابع مشابه
Joint large deviation result for empirical measures of the coloured random geometric graphs
We prove joint large deviation principle for the empirical pair measure and empirical locality measure of the near intermediate coloured random geometric graph models on n points picked uniformly in a d-dimensional torus of a unit circumference. From this result we obtain large deviation principles for the number of edges per vertex, the degree distribution and the proportion of isolated vertic...
متن کاملLarge Deviation Principles for Empirical Measures of Coloured Random Graphs
Abstract. For any finite coloured graph we define the empirical neighbourhood measure, which counts the number of vertices of a given colour connected to a given number of vertices of each colour, and the empirical pair measure, which counts the number of edges connecting each pair of colours. For a class of models of sparse coloured random graphs, we prove large deviation principles for these ...
متن کاملJoint Large Deviation principle for empirical measures of the d-regular random graphs
For a $d-$regular random model, we assign to vertices $q-$state spins. From this model, we define the \emph{empirical co-operate measure}, which enumerates the number of co-operation between a given couple of spins, and \emph{ empirical spin measure}, which enumerates the number of sites having a given spin on the $d-$regular random graph model. For these empirical measures we obtain large devi...
متن کاملLarge Deviations in Randomly Coloured Random Graphs
Models of random graphs are considered where the presence or absence of an edge depends on the random types (colours) of its vertices, so that whether or not edges are present can be dependent. The principal objective is to study large deviations in the number of edges. These graphs provide a natural example with two different non-degenerate large deviation regimes, one arising from large devia...
متن کاملLarge deviation principles for empirical measures of the multitype random networks
In this article we study the stochastic block model also known as the multi-type random networks (MRNs). For the stochastic block model or the MRNs we define the empirical group measure, empirical cooperative measure and the empirical locality measure. We derive large deviation principles for the empirical measures in the weak topology. These results will form the basis of understanding asympto...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SpringerPlus
سال: 2016
ISSN: 2193-1801
DOI: 10.1186/s40064-016-2718-z