World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
40
Citations
8812
World Ranking
2013
National Ranking
850

Russell Lyons publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Russell Lyons sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 82 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 141 publications — 33rd percentile

33% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Russell Lyons D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Russell Lyons sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 137 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 40 D-Index — 45th percentile

45% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society
  • 1990 - Fellow of Alfred P. Sloan Foundation

Overview

Russell Lyons is affiliated with Indiana University in the United States and works primarily in the field of mathematics. Their research spans multiple subfields including mathematical physics, geometry and topology, statistics and probability, molecular biology, and applied mathematics.

The main subjects of their research include stochastic processes and statistical mechanics, Markov chains and Monte Carlo methods, geometric and algebraic topology, mathematical dynamics and fractals, point processes and geometric inequalities, theoretical and computational physics, and algorithms and data compression.

Russell Lyons has published extensively, with notable papers including:

  • Poisson boundaries of lamplighter groups: proof of the Kaimanovich-Vershik conjecture (2020, Journal of the European Mathematical Society)
  • Lower bounds for trace reconstruction (2020, The Annals of Applied Probability)
  • Induced graphs of uniform spanning forests (2020, Annales de l'Institut Henri Poincaré Probabilités et Statistiques)
  • A reverse Aldous-Broder algorithm (2021, Annales de l'Institut Henri Poincaré Probabilités et Statistiques)
  • Explicit universal minimal constants for polynomial growth of groups (2022, Journal of Group Theory)

The scientist frequently collaborates with several co-authors, including Yuval Peres, Nina Holden, Xin Sun, Avinoam Mann, and Romain Tessera.

Russell Lyons has contributed to an array of publication venues, with multiple works appearing in:

  • arXiv (Cornell University)
  • The Annals of Applied Probability
  • Annales de l'Institut Henri Poincaré Probabilités et Statistiques
  • The Annals of Probability
  • Journal of the European Mathematical Society

Awards granted to Russell Lyons include the fellowship of the American Mathematical Society in 2013 and the Alfred P. Sloan Foundation fellowship in 1990.

Best Publications

  • Probability on Trees and Networks

    Russell Lyons;Yuval Peres

  • Processes on Unimodular Random Networks

    David J. Aldous;Russell Lyons

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

    Russell Lyons;Robin Pemantle;Yuval Peres

  • Random Walks and Percolation on Trees

    Russell Lyons

  • Distance covariance in metric spaces

    Russell Lyons

  • Determinantal probability measures

    Russell Lyons;Russell Lyons

  • Uniform spanning forests

    Itai Benjamini;Russell Lyons;Yuval Peres;Oded Schramm

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

    Russell Lyons

  • Asymptotic Enumeration of Spanning Trees

    Russell Lyons

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

    Russell Lyons

  • Group-invariant Percolation on Graphs

    I. Benjamini;R. Lyons;Y. Peres;O. Schramm

  • Random Walks, Capacity and Percolation on Trees

    Russell Lyons

  • Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure

    Russell Lyons;Robin Pemantle;Yuval Peres

  • The Ising model and percolation on trees and tree-like graphs

    Russell Lyons

  • Random Walk in a Random Environment and First-Passage Percolation on Trees

    Russell Lyons;Robin Pemantle

  • Biased random walks on Galton-Watson trees

    Russell Lyons;Robin Pemantle;Yuval Peres

  • Phase transitions on nonamenable graphs

    Russell Lyons

  • Indistinguishability of Percolation Clusters

    Russell Lyons;Oded Schramm

  • A Conceptual Proof of the Kesten-Stigum Theorem for Multi-Type Branching Processes

    Thomas Kurtz;Russell Lyons;Robin Pemantle;Yuval Peres

  • A measurable-group-theoretic solution to von Neumann’s problem

    Damien Gaboriau;Russell Lyons

Frequent Co-Authors

Oded Schramm
Oded Schramm Microsoft (United States)
Robin Pemantle
Robin Pemantle University of Pennsylvania
Itai Benjamini
Itai Benjamini Weizmann Institute of Science
David Aldous
David Aldous University of California, Berkeley
Kevin Zumbrun
Kevin Zumbrun Indiana University
Peter Winkler
Peter Winkler Dartmouth College
Alexander S. Kechris
Alexander S. Kechris California Institute of Technology
Charles Radin
Charles Radin The University of Texas at Austin
Fedor Nazarov
Fedor Nazarov Kent State University
Thomas G. Kurtz
Thomas G. Kurtz University of Wisconsin–Madison

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