Connectivity of a Gaussian network
Following Etherington, Hoge and Parkes, we consider a network consisting of (approximately) N transceivers in the plane R 2 distributed randomly with density given by a Gaussian distribution about the origin, and assume each transceiver can communicate with all other transceivers within distance s. We give bounds for the distance from the origin to the furthest transceiver connected to the origin, and that of the closest transceiver that is not connected to the origin.. He received PhDs from Eotvos Uni-versity, Budapest, Hungary and the University of Cambridge, England. He works in extremal and probabilistic combinatorics, polynomials of graphs, combinatorial prob-ability and percolation theory. He has written eight books, including Extremal Graph Theory, Random Graphs and Modern Graph Theory, and over 300 research papers. He has supervised over forty doctoral students, many of whom hold leading positions in prominent universities throughout the world. Paul Balister is a Professor at the University of Memphis, where he has been since 1998. He obtained his PhD from the University of Cambridge, England in 1992 and subsequently held positions at Harvard and Cambridge. He has worked in algebraic number theory, combinatorics, graph theory and probability theory. Amites Sarkar is a Visiting Assistant Professor at the University of Memphis. He ob-tained his PhD from the University of Cambridge in 1998, and has been at Memphis since 2003. He has worked in combinatorics and probability theory. Mark Walters is a Teaching Fellow at Peterhouse College, Cambridge. He obtained his PhD from the University of Cambridge in 2000, and was a Research Fellow of Trinity College, Cambridge. He has worked in combinatorics and probability theory.