Russell Lyons | Academic Influence

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Russell Lyons

Mathematics

#5119

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#7236

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Measure Theory

#2461

World Rank

#2956

Historical Rank

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Mathematics

Russell Lyons's Degrees

Bachelors Mathematics University of California, Berkeley

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Why Is Russell Lyons Influential?

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According to Wikipedia, Russell David Lyons is an American mathematician, specializing in probability theory on graphs, combinatorics, statistical mechanics, ergodic theory and harmonic analysis. Lyons graduated with B.A. mathematics in 1979 from Case Western Reserve University, where he became a Putnam Fellow in 1977 and 1978. He received his Ph.D. in 1983 from the University of Michigan with the thesis A Characterization of Measures Whose Fourier-Stieltjes Transforms Vanish at Infinity, which was supervised by Hugh L. Montgomery and Allen Shields. Lyons was a postdoc for the academic year 1984–1985 at the University of Paris-Sud. He was an assistant professor at Stanford University from 1985 to 1990 and an associate professor at Indiana University from 1990 to 1994. At Georgia Tech he was a full professor from 2000 to 2003. At Indiana University he was a professor of mathematics from 1994 to 2014 and is since 2014 the James H. Rudy Professor of Mathematics; there he has also been an adjunct professor of statistics since 2006.

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Russell Lyons's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Probability on Trees and Networks (2017) (709)
Processes on Unimodular Random Networks (2006) (454)
Conceptual proofs of L log L criteria for mean behavior of branching processes (1995) (446)
Random Walks and Percolation on Trees (1990) (384)
Determinantal probability measures (2002) (258)
Uniform spanning forests (2001) (249)
A Simple Path to Biggins’ Martingale Convergence for Branching Random Walk (1998) (246)
Group-invariant Percolation on Graphs (1999) (237)
Asymptotic Enumeration of Spanning Trees (2002) (210)
The Spread of Evidence-Poor Medicine via Flawed Social-Network Analysis (2010) (195)
Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure (1995) (189)
Random Walks, Capacity and Percolation on Trees (1992) (181)
Biased random walks on Galton–Watson trees (1996) (127)
Phase transitions on nonamenable graphs (1999) (124)
The Ising model and percolation on trees and tree-like graphs (1989) (122)
A measurable-group-theoretic solution to von Neumann’s problem (2007) (117)
A Conceptual Proof of the Kesten-Stigum Theorem for Multi-Type Branching Processes (1997) (115)
Indistinguishability of Percolation Clusters (1998) (107)
Random walk in a random environment and rst-passage percolation on trees (2004) (95)
Strong laws of large numbers for weakly correlated random variables. (1988) (93)
Distance covariance in metric spaces (2011) (86)
Random walks on the lamplighter group (1996) (78)
Perfect matchings as IID factors on non-amenable groups (2009) (78)
Percolation Perturbations in Potential Theory and Random Walks (1998) (72)
Critical Percolation on any Nonamenable Group has no Infinite Clusters (2011) (69)
Correction: Random walk in a random environment and first-passage percolation on trees (1992) (68)
Minimal spanning forests (2004) (65)
On measures simultaneously 2- and 3-invariant (1988) (64)
Stationary determinantal processes: Phase multiplicity, Bernoullicity, entropy, and domination (2002) (64)
Explicit Isoperimetric Constants and Phase Transitions in the Random-Cluster Model (2000) (56)
Random Orderings and Unique Ergodicity of Automorphism Groups (2012) (56)
Unimodular random trees (2012) (54)
Random Complexes and l^2-Betti Numbers (2008) (52)
Ends in Uniform Spanning Forests (2007) (48)
Random walks and the growth of groups (1995) (46)
A bird's-eye view of uniform spanning trees and forests (1997) (44)
UNSOLVED PROBLEMS CONCERNING RANDOM WALKS ON TREES (1997) (44)
Amenability, Kazhdan’s property and percolation for trees, groups and equivalence relations (1991) (43)
Factors of IID on Trees (2014) (42)
Determinantal Probability: Basic Properties and Conjectures (2014) (39)
Lower bounds for trace reconstruction (2018) (38)
Identities and Inequalities for Tree Entropy (2007) (35)
Crossing Estimates and Convergence of Dirichlet Functions Along Random Walk and Diffusion Paths (1999) (34)
Sharp Bounds on Random Walk Eigenvalues via Spectral Embedding (2012) (34)
Fourier-Stieltjes Coefficients and Asymptotic Distribution Modulo 1 (1985) (29)
Recurrence of random walk traces (2006) (27)
A Computer Proof of a Series Evaluation in Terms of Harmonic Numbers (2002) (27)
Markov chain intersections andtheloop-erased walk (2001) (27)
Fluid-solid transition in a hard-core system. (2005) (25)
Resistance Bounds for First-Passage Percolation and Maximum Flow (1999) (22)
Coupling and Bernoullicity in random-cluster and Potts models (2001) (22)
Singularity of Some Random Continued Fractions (1999) (22)
Poisson splitting by factors (2009) (21)
High-precision entropy values for spanning trees in lattices (2003) (20)
Growth of the Number of Spanning Trees of the Erdős–Rényi Giant Component (2007) (18)
Equivalence of boundary measures on covering trees of finite graphs (1994) (18)
The measure of non-normal sets (1986) (17)
Errata to “Distance covariance in metric spaces” (2018) (17)
A lower bound on the Cesàro operator (1982) (17)
A Note on Tail Triviality for Determinantal Point Processes (2018) (16)
A transient Markov chain with finitely many cutpoints (2007) (16)
Characterizations of measures whose Fourier-Stieltjes transforms vanish at infinity (1984) (16)
RandomWalks and Electric Networks (2016) (15)
Invariant coupling of determinantal measures on sofic groups (2014) (14)
UNIFORM NON-AMENABILITY, COST, AND THE FIRST ℓ 2 -BETTI NUMBER (2007) (14)
Change Intolerance in Spanning Forests (2001) (14)
Stationary measures for random walks in a random environment with random scenery. (1999) (13)
New Mössbauer-Effect Measurements onFe57in a Ni Host: The Critical Exponentβfor Ni (1972) (13)
A new type of sets of uniqueness (1988) (12)
The size of some classes of thin sets (1987) (12)
Poisson boundaries of lamplighter groups: proof of the Kaimanovich–Vershik conjecture (2015) (12)
Ordinal rankings on measures annihilating thin sets (1988) (10)
Szegő limit theorems (2002) (10)
Fixed price of groups and percolation (2011) (9)
Homogeneous partial derivatives of radial functions (1994) (9)
Ladder Sandpiles (2007) (9)
A Solidification Phenomenon in Random Packings (2005) (9)
Diffusions and Random Shadows in Negatively Curved Manifolds (1996) (9)
Hyperbolic Space Has Strong Negative Type (2014) (9)
Coalescing Particles on an Interval (1999) (8)
Regional Economic Integration (1999) (7)
A reverse Aldous–Broder algorithm (2019) (7)
Mixing and asymptotic distribution modulo 1 (1988) (7)
Upper bounds for the spectral function on homogeneous spaces via volume growth (2017) (6)
Cycle density in infinite Ramanujan graphs (2013) (6)
Occupation measure of random walks and wired spanning forests in balls of Cayley graphs (2017) (5)
Stationary Determinantal Processes: Phase Transitions, Bernoullicity, Entropy, and Domination (2002) (4)
Measure-theoretic quantifiers and Haar measure (1982) (4)
Conceptual Proofs of L log L Criteria (2004) (3)
Uniform Non-amenability and the First ℓ 2 -betti Number (3)
Shorter Notes: A Lower Bound on the Cesaro Operator (1982) (3)
Induced graphs of uniform spanning forests (2018) (3)
Strong negative type in spheres (2019) (3)
Szeg˝ O Limit Theorems (2003) (3)
Explicity isoperimetric constants, phase transitions in the random-cluster and Potts models, and Bernoullicity (2000) (3)
Zero Sets for Spaces of Analytic Functions (2017) (2)
The local structure of some measure-algebra homomorphisms. (1991) (2)
Exit boundaries of multidimensional SDEs (2019) (2)
Probabilistic Aspects of Infinite Trees and Some Applications (1996) (2)
Comparing Graphs of Different Sizes (2016) (2)
Crowdfunding to take-off in Australia? (2015) (1)
When does a branching process grow like its mean? Conceptual proofs of L log L criteria (1994) (1)
Topologies on measure spaces and the Radon-Nikodym theorem (1988) (1)
Reduced power operations in motivic cohomology . Motivic cohomology with z/2-coefficients . A conformally invariant sphere theorem in four dimensions . Tameness on the boundary and Ahlfors' measure conjecture . Determinantal probability measures (2003) (1)
Monotonicity for continuous-time random walks (2021) (1)
SINGULAR MEASURES WITH SPECTRAL GAPS (1988) (1)
Monotonicity of average return probabilities for random walks in random environments (2017) (1)
Second errata to “Distance covariance in metric spaces” (2021) (1)
Erratum: “Measure-theoretic quantifiers and Haar measure” [Proc. Amer. Math. Soc. 86\ (1982) no. 1, 67–70; MR0663868 (83i:43001)] (1984) (1)
On the structure of sets of uniqueness (1987) (1)
Explicit universal minimal constants for polynomial growth of groups (2020) (1)
Corrected Entropy Values for Spanning Trees in Lattices (2003) (1)
Ends in Uniform Spanning Forests 1 by (2008) (1)
A stationary planar random graph with singular stationary dual: dyadic lattice graphs (2018) (1)
ERRATUM TO "MEASURE-THEORETIC QUANTIFIERS AND HAAR MEASURE" (1984) (1)
A calculus proof of the Cram\'er-Wold theorem (2016) (1)
Second Errata to “Processes on Unimodular Random Networks” (2019) (0)
Uniform Spanning Trees (2016) (0)
1 1 O ct 2 02 0 ON THE MINIMAL GROWTH OF FINITELY GENERATED GROUPS (2020) (0)
How Fast and where does a Random Walker Move on a Random Tree (1996) (0)
Errata to “Processes on unimodular random networks” (2017) (0)
FIRST-PASSAGE PERCOLATION ON TREES' (2016) (0)
Errata to “Wiener’s theorem, the Radon-Nikodym theorem, andMo(T)” (1988) (0)
Capacity and Stochastic Processes (2016) (0)
Power of polledness (2018) (0)
Processes and Related Fields Ladder Sandpiles (2007) (0)
Submitted to the Annals of Probability ERRATA TO “ DISTANCE COVARIANCE IN METRIC SPACES ” By (2017) (0)
On the minimal growth of finitely generated groups (2020) (0)
Percolation on Transitive Graphs (2016) (0)
DISTANCE COVARIANCE IN METRIC SPACES1 BY RUSSELL LYONS (2013) (0)
Normality of tree-growing search strategies (1998) (0)
Escape Rate of Random Walks and Embeddings (2016) (0)
Percolation beyond 7 l d : the contributions of Oded Schramm (2011) (0)
PR ] 2 4 Ju l 2 01 9 A Reverse Aldous / Broder Algorithm (2019) (0)
Th e Review: A Journal of Undergraduate Student Research (1999) (0)
Infinite Electrical Networks and Dirichlet Functions (2016) (0)
RandomWalks on Groups and Poisson Boundaries (2016) (0)
Wiener's theorem, the Radon-Nikodym theorem, andm0(T) (1985) (0)
The Mass-Transport Technique and Percolation (2016) (0)
Determinantal Probability Measures by Russell Lyons (0)
Group-Invariant Percolation on Graphs by Itai Benjamini (2016) (0)
Branching Processes, Second Moments, and Percolation (2016) (0)
Erratum to “Lower bounds for trace reconstruction” (2022) (0)
Limit Theorems for Galton-Watson Processes (2016) (0)
PR ] 2 4 A ug 2 00 0 Explicit isoperimetric constants , phase transitions in the random-cluster and Potts models , and Bernoullicity (2000) (0)
Glossary of Notation (2016) (0)
A stationary planar random graph with singular stationary dual: dyadic lattice graphs (2019) (0)
Recurrence of Random Walk Traces 1 (2007) (0)
Ideal Poisson-Voronoi tessellations on hyperbolic spaces, I (2023) (0)
Comments on Exercises (2017) (0)
RandomWalks on Galton-Watson Trees (2016) (0)
Percolation Perturbations inPotential Theory and Random (1998) (0)

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