Abstract:
We consider the rank-1 inhomogeneous random graph in the critical window, where a vertex i is assigned a weight w_i and an edge (i,j) is present with probability \exp(-C w_i w_j), independent of other edges. Under third moment assumptions on the weights, Aldous'97 showed that the ordered sequence of component weights converge in l2 to the lengths of ordered excursions of a brownian motion with parabolic drift. We obtain the same result for ordered component sizes, and further show that for large components, this ranking by weights and sizes agree with high probability.
Biography:
Prabhanka Deka is a postdoctoral fellow at the Beijing International Center for Mathematical Research, Peking University. He obtained his Bachelors and Masters in Mathematics from Indian Statistical Institute, Bangalore, and his PhD from the Department of Statistics and Operations Research at University of North Carolina, Chapel Hill, under the supervision of Sayan Banerjee and Mariana Olvera-Cravioto. His research interests include probability theory and applications, focusing on properties of large random graphs and networks, and processes on them.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
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