Ningyuan Chen

Directed Random Graphs with given Degree Distributions

Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that is, from which a simple directed graph can be drawn. We then analyze a directed version of the configuration model and show that, provided that F and G have finite variance, the probability of obtaining a simple graph is bounded away from zero as the number of nodes grows. We show that conditional on the resulting graph being simple, the in- and out-degree distributions are (approximately) F and G for large size graphs. Moreover, when the degree distributions have only finite mean we show that the elimination of self-loops and multiple edges does not significantly change the degree distributions in the resulting simple graph.

Efficient simulation for branching linear recursions

We provide an algorithm for simulating the unique attracting fixed-point of linear branching distributional equations. Such equations appear in the analysis of information ranking algorithms, e.g., PageRank, and in the complexity analysis of divide and conquer algorithms, e.g., Quicksort. The naive simulation approach would be to simulate exactly a suitable number of generations of a weighted branching process, which has exponential complexity in the number of generations being sampled. Instead, we propose an iterative bootstrap algorithm that has linear complexity; we prove its convergence and the consistency of a family of estimators based on our approach.

Ranking algorithms on directed configuration networks

This paper studies the distribution of a family of rankings, which includes Google’s PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable

PageRank in Scale-Free Random Graphs

R^*

A Partitioning Algorithm for Markov Decision Processes with Applications to Market Microstructure

that can be written as a linear combination of i.i.d. copies of the endogenous solution to a stochastic fixed point equation of the form

Coupling on weighted branching trees

R \stackrel {D}{=} \sum^N _{i=1} C_iR_i + Q,

Generalized PageRank on Directed Configuration Networks

where

Welfare Analysis of Dynamic Pricing

(Q,N, \{C_i\})

Duopoly Competition with Network Effects in Discrete Choice Models

is a real-valued vector with

Does the Prohibition of Trade-Through Hurt Liquidity Demanders?

N \in \{0, 1, 2, ... \}