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We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to showâ€¦ (More)

- Nathan Ross
- 2011

Abstract: This survey article discusses the main concepts and techniques of Steinâ€™s method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and alsoâ€¦ (More)

We develop a new formulation of Steinâ€™s method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our frameworkâ€¦ (More)

We study the joint degree counts in linear preferential attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence withâ€¦ (More)

- Elchanan Mossel, Nathan Ross
- ArXiv
- 2015

We consider the problem of reconstructing graphs or labeled graphs from neighborhoods of a given radius r. Special instances of this problem include DNA shotgun assembly, neural networkâ€¦ (More)

- Holger Paul Keeler, Nathan Ross, Aihua Xia
- ArXiv
- 2014

We consider the point process of signal strengths from transmitters in a wireless network observed from a fixed position under models with general signal path loss and random propagation effects. Weâ€¦ (More)

- Nathan Ross, Dominic Schuhmacher
- IEEE Transactions on Information Theory
- 2017

We consider the point process of signal strengths emitted from transmitters in a wireless network and observed at a fixed position. In our model, transmitters are placed deterministically or randomlyâ€¦ (More)

Consider the setting of sparse graphs on N vertices, where the vertices have distinct " names " , which are strings of length O(log N) from a fixed finite alphabet. For many natural probabilityâ€¦ (More)

- Jason Fulman, Nathan Ross
- 2012

We derive a new result for exponential approximation using Steinâ€™s method of exchangeable pairs. As an application, an exponential limit theorem with error term is derived for |Tr(U)|, where Tr(U)â€¦ (More)

- Nathan Ross
- Combinatorics, Probability & Computing
- 2009

Steinâ€™s method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair isâ€¦ (More)