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Robert Adler

Publications and source records attributed to Robert Adler.

4 recordsLinked to original sources
arXiv2016

On the evolution of topology in dynamic clique complexes

We consider a time varying analogue of the Erd{\H o}s-R{\' e}nyi graph and study the topological variations of its associated clique complex. The dynamics of the graph are stationary and are determined by the edges, which evolve independently as continuous time Markov chains. Our main result is that when the edge inclusion probability is of the form $p = n^α$, where $n$ is the number of vertices and $α\in (-1/k, -1/(k + 1)),$ then the process of the normalized $k-$th Betti number of these dynamic clique complexes converges weakly to the Ornstein-Uhlenbeck process as $n \to \infty.$

math.PR↗
arXiv2015

Climbing down Gaussian peaks

How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new light in existence of holes. How likely is the field to be above a high level on one compact set (e.g. a sphere) and to be below a fraction of that level on some other compact set, e.g. at the center of the corresponding ball? How likely is the field to be below that fraction of the level {\it anywhere} inside the ball? We work on the level of large deviations.

math.PR↗
arXiv2009

Citation Statistics

This is a report about the use and misuse of citation data in the assessment of scientific research. The idea that research assessment must be done using ``simple and objective'' methods is increasingly prevalent today. The ``simple and objective'' methods are broadly interpreted as bibliometrics, that is, citation data and the statistics derived from them. There is a belief that citation statistics are inherently more accurate because they substitute simple numbers for complex judgments, and hence overcome the possible subjectivity of peer review. But this belief is unfounded.

stat.ME↗