Kwabena Doku-Amponsah

Large deviation principles for empirical measures of colored random graphs

For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degree distribution of Erdos-Renyi graphs near criticality.

LOSSY ASYMPTOTIC EQUIPARTITION PROPERTY FOR HIERARCHICAL DATA STRUCTURES

This paper presents a rate-distortion theory for hierarchical networked data structures modelled as tree-indexed multitype process. To be specific, this paper gives a generalized Asymptotic Equipartition Property (AEP) for the Process. The general methodology of proof of the AEP are process level large deviation principles for suitably defined empirical measures for muiltitype Galton-Watson trees.

Modeling inflation rates and exchange rates in Ghana: application of multivariate GARCH models

This paper was aimed at investigating the volatility and conditional relationship among inflation rates, exchange rates and interest rates as well as to construct a model using multivariate GARCH DCC and BEKK models using Ghana data from January 1990 to December 2013. The study revealed that the cumulative depreciation of the cedi to the US dollar from 1990 to 2013 is 7,010.2% and the yearly weighted depreciation of the cedi to the US dollar for the period is 20.4%. There was evidence that, the fact that inflation rate was stable, does not mean that exchange rates and interest rates are expected to be stable. Rather, when the cedi performs well on the forex, inflation rates and interest rates react positively and become stable in the long run. The BEKK model is robust to modelling and forecasting volatility of inflation rates, exchange rates and interest rates. The DCC model is robust to model the conditional and unconditional correlation among inflation rates, exchange rates and interest rates. The BEKK model, which forecasted high exchange rate volatility for the year 2014, is very robust for modelling the exchange rates in Ghana. The mean equation of the DCC model is also robust to forecast inflation rates in Ghana.

Large Deviation Result for the Empirical Locality Measure of Typed Random Geometric Graphs

Abstract. In this article for a finite typed random geometric graph we define the empirical locality distribution, which records the number of nodes of a given type linked to a given number of nodes of each type. We find large deviation principle (LDP) for the empirical locality measure given the empirical pair measure and the empirical type measure of the typed random geometric graphs. From this LDP, we derive large deviation principles for the degree measure and the proportion of detached nodes in the classical Erdős-Rényi graph defined on [0, 1]. This graphs have been suggested by (Canning and Penman, 2003) as a possible extension to the randomly typed random graphs.

Asymptotic equipartition properties for simple hierarchical and networked structures

We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large

Lossy Asymptotic Equipartition Property for Networked Data Structures

n

LARGE DEVIATION RESULTS FOR CRITICAL MULTITYPE GALTON-WATSON TREES

, a networked data structure consisting of

ASYMPTOTICS OF THE PARTITION FUNCTION OF ISING MODEL ON INHOMOGENEOUS RANDOM GRAPHS

n

Joint large deviation result for empirical measures of the coloured random geometric graphs.

units connected by an average number of links of order

Large Deviation Principle for the Empirical Degree Measure of Preferential Attachment Random Graphs

n/log n