
Minimum stationary values of sparse random directed graphs
We consider the stationary distribution of the simple random walk on the...
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Provable and practical approximations for the degree distribution using sublinear graph samples
The degree distribution is one of the most fundamental properties used i...
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Degrees of randomized computability: decomposition into atoms
In this paper we study structural properties of LVdegrees of the algebr...
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Fast mixing via polymers for random graphs with unbounded degree
The polymer model framework is a classical tool from statistical mechani...
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A Liouville principle for the random conductance model under degenerate conditions
We consider a random conductance model on the ddimensional lattice, d∈[...
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Engineering Uniform Sampling of Graphs with a Prescribed Powerlaw Degree Sequence
We consider the following common network analysis problem: given a degre...
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The giant component of the directed configuration model revisited
We prove a law of large numbers for the order and size of the largest st...
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Rankings in directed configuration models with heavy tailed indegrees
We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the indegree sequence. The graphs are generated by the directed configuration model. Under the assumption of bounded (2+η)moments on the indegrees and of bounded outdegrees, we obtain tight comparisons between the maximum value of the stationary distribution and the maximum indegree. Under the further assumption that the order statistics of the indegrees have a powerlaw behavior, we show that the extremal values of the stationary distribution also have a powerlaw behavior with the same index. In the same setting, we prove that these results extend to the PageRank scores of the random digraph, thus confirming a version of the socalled powerlaw hypothesis. Along the way, we establish several facts about the model, including the mixing time cutoff and the characterization of the typical values of the stationary distribution, which were previously obtained under the assumption of bounded indegrees.
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