D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 36 Citations 7,493 104 World Ranking 1347 National Ranking 589

Research.com Recognitions

Awards & Achievements

2013 - Fellow of the American Mathematical Society

1990 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Combinatorics
  • Real number

Russell Lyons mostly deals with Discrete mathematics, Combinatorics, Random walk, Random graph and Percolation. His studies deal with areas such as Completeness, Group representation and Homology as well as Discrete mathematics. His work on Unimodular matrix, Pathwidth and Spanning tree as part of general Combinatorics study is frequently linked to Continuum percolation theory and Symmetric graph, therefore connecting diverse disciplines of science.

His Random walk research incorporates themes from Galton watson, Hausdorff dimension and Harmonic measure. His Percolation research includes themes of Tree and Statistical physics. His research investigates the connection between Cayley graph and topics such as Isoperimetric inequality that intersect with issues in Omega, Automorphism, Invariant and Embedding.

His most cited work include:

  • Probability on Trees and Networks (436 citations)
  • Processes on Unimodular Random Networks (405 citations)
  • Conceptual proofs of L log L criteria for mean behavior of branching processes (393 citations)

What are the main themes of his work throughout his whole career to date?

Combinatorics, Discrete mathematics, Random walk, Pure mathematics and Spanning tree are his primary areas of study. His work deals with themes such as Measure, Mathematical proof and Markov chain, which intersect with Discrete mathematics. His work carried out in the field of Random walk brings together such families of science as Hausdorff dimension and First passage percolation.

His Pure mathematics research is multidisciplinary, incorporating perspectives in Function, Uniqueness and Space. The Spanning tree study combines topics in areas such as Giant component, Entropy, Connectivity and Minimum spanning tree. His Probability measure study which covers Point process that intersects with Triviality, Completeness, Group representation, Matroid and Homology.

He most often published in these fields:

  • Combinatorics (47.28%)
  • Discrete mathematics (45.11%)
  • Random walk (25.00%)

What were the highlights of his more recent work (between 2016-2021)?

  • Combinatorics (47.28%)
  • Random walk (25.00%)
  • Pure mathematics (18.48%)

In recent papers he was focusing on the following fields of study:

His scientific interests lie mostly in Combinatorics, Random walk, Pure mathematics, Set and Unimodular matrix. His Combinatorics study frequently draws connections between related disciplines such as Probability measure. His Random walk study incorporates themes from Discrete mathematics, Degree, Entropy, Polynomial and Cayley graph.

The study incorporates disciplines such as Embedding and Mathematical proof in addition to Discrete mathematics. His study in the field of Conjecture, Analytic function and Harmonic measure is also linked to topics like Volume growth. The various areas that Russell Lyons examines in his Unimodular matrix study include Equivalence relation, Dual polyhedron, Percolation and Transitive relation.

Between 2016 and 2021, his most popular works were:

  • Probability on Trees and Networks (436 citations)
  • Factors of IID on Trees (25 citations)
  • Lower bounds for trace reconstruction (19 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Combinatorics
  • Real number

Russell Lyons mainly investigates Upper and lower bounds, Combinatorics, Discrete mathematics, Eigenvalues and eigenvectors and Trace. His Combinatorics research is multidisciplinary, relying on both Ergodic theory and Entropy. The concepts of his Discrete mathematics study are interwoven with issues in Embedding, Mathematical proof, Random walk and Statistical hypothesis testing.

His Embedding research incorporates themes from Stochastic process, Random graph and Isoperimetric inequality. His Random walk research includes themes of Cayley graph, Spectrum, Markov chain and Spanning tree. Russell Lyons combines subjects such as Spectral function, Operator, Heat kernel and Pure mathematics with his study of Eigenvalues and eigenvectors.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Probability on Trees and Networks

Russell Lyons;Yuval Peres.
(2017)

1093 Citations

Random Walks and Percolation on Trees

Russell Lyons.
Annals of Probability (1990)

433 Citations

Conceptual proofs of L log L criteria for mean behavior of branching processes

Russell Lyons;Robin Pemantle;Yuval Peres.
Annals of Probability (1995)

421 Citations

Processes on Unimodular Random Networks

David J. Aldous;Russell Lyons.
Electronic Journal of Probability (2007)

419 Citations

A Simple Path to Biggins’ Martingale Convergence for Branching Random Walk

Russell Lyons.
Institute for Mathematics and Its Applications (1997)

247 Citations

Determinantal probability measures

Russell Lyons;Russell Lyons.
Publications Mathématiques de l'IHÉS (2003)

241 Citations

Uniform spanning forests

Itai Benjamini;Russell Lyons;Yuval Peres;Oded Schramm.
Annals of Probability (2001)

230 Citations

The Spread of Evidence-Poor Medicine via Flawed Social-Network Analysis

Russell Lyons.
Statistics, Politics, and Policy (2011)

225 Citations

Group-invariant Percolation on Graphs

I. Benjamini;R. Lyons;Y. Peres;O. Schramm.
Geometric and Functional Analysis (1999)

213 Citations

Asymptotic Enumeration of Spanning Trees

Russell Lyons.
Combinatorics, Probability & Computing (2005)

213 Citations

Best Scientists Citing Russell Lyons

Itai Benjamini

Itai Benjamini

Weizmann Institute of Science

Publications: 55

Robin Pemantle

Robin Pemantle

University of Pennsylvania

Publications: 55

Elchanan Mossel

Elchanan Mossel

MIT

Publications: 37

Geoffrey Grimmett

Geoffrey Grimmett

University of Cambridge

Publications: 32

Simon R. Harris

Simon R. Harris

Wellcome Sanger Institute

Publications: 26

Oded Schramm

Oded Schramm

Microsoft (United States)

Publications: 23

Andreas E. Kyprianou

Andreas E. Kyprianou

University of Bath

Publications: 22

Svante Janson

Svante Janson

Uppsala University

Publications: 22

Allan Sly

Allan Sly

Princeton University

Publications: 17

James R. Lee

James R. Lee

University of Washington

Publications: 15

Ofer Zeitouni

Ofer Zeitouni

Weizmann Institute of Science

Publications: 15

Martin T. Barlow

Martin T. Barlow

University of British Columbia

Publications: 15

László Lovász

László Lovász

Eötvös Loránd University

Publications: 15

Gábor Székely

Gábor Székely

ETH Zurich

Publications: 14

Alexander S. Kechris

Alexander S. Kechris

California Institute of Technology

Publications: 14

Amir Dembo

Amir Dembo

Stanford University

Publications: 14

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

If you think any of the details on this page are incorrect, let us know.

Contact us
Something went wrong. Please try again later.