Scott Sheffield | Academic Influence

Scott Sheffield's AcademicInfluence.com Rankings

Scott Sheffield

Mathematics

#1860

World Rank

#2958

Historical Rank

#753

USA Rank

Measure Theory

#2815

World Rank

#3353

Historical Rank

#814

USA Rank

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Mathematics

Scott Sheffield's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics Stanford University

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Why Is Scott Sheffield Influential?

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According to Wikipedia, Scott Sheffield is a professor of mathematics at the Massachusetts Institute of Technology. His primary research field is theoretical probability. Research Much of Sheffield's work examines conformal invariant objects which arise in the study of two-dimensional statistical physics models. He studies the Schramm-Loewner evolution SLE and its relations to a variety of other random objects. For example, he proved that SLE describes the interface between two Liouville quantum gravity surfaces that have been conformally welded together. In joint work with Oded Schramm, he showed that contour lines of the Gaussian free field are related to SLE. With Jason Miller, he developed the theory of Gaussian free field flow lines, which include SLE for all values of κ, as well as many variants of SLE.

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Scott Sheffield'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

Dimers and amoebae (2003) (511)
Gaussian free fields for mathematicians (2003) (455)
Liouville quantum gravity and KPZ (2008) (453)
Tug-of-war and the infinity Laplacian (2006) (418)
Contour lines of the two-dimensional discrete Gaussian free field (2006) (294)
Conformal weldings of random surfaces: SLE and the quantum gravity zipper (2010) (270)
Imaginary geometry I: interacting SLEs (2012) (249)
Tug-of-war with noise: A game-theoretic view of the $p$-Laplacian (2006) (226)
Liouville quantum gravity as a mating of trees (2014) (222)
Exploration trees and conformal loop ensembles (2006) (214)
Conformal loop ensembles: the Markovian characterization and the loop-soup construction (2010) (205)
A contour line of the continuum Gaussian free field (2010) (182)
Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees (2013) (173)
Random Surfaces (2003) (165)
Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012) (159)
Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric (2015) (157)
Harmonic explorer and its convergence to SLE4 (2003) (138)
Quantum Loewner Evolution (2013) (129)
Liouville quantum gravity and the Brownian map III: the conformal structure is determined (2016) (128)
Imaginary geometry II: Reversibility of SLEκ(ρ1;ρ2) for κ∈(0,4). (2016) (120)
Renormalization of Critical Gaussian Multiplicative Chaos and KPZ Relation (2014) (120)
Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces (2004) (119)
Imaginary geometry III: reversibility of SLE_κ for κ\in (4,8) (2016) (119)
Liouville quantum gravity and the Brownian map II: Geodesics and continuity of the embedding (2016) (105)
Quantum gravity and inventory accumulation (2011) (100)
Fractional Gaussian fields: A survey (2014) (82)
Logarithmic fluctuations for internal DLA (2010) (76)
An axiomatic characterization of the Brownian map (2015) (75)
Conformal Radii for Conformal Loop Ensembles (2006) (73)
Bipolar orientations on planar maps and SLE$_{12}$ (2015) (65)
Log-correlated Gaussian fields: an overview (2014) (59)
Vector‐valued optimal Lipschitz extensions (2010) (58)
Internal DLA and the Gaussian free field (2011) (57)
The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity (2017) (53)
Liouville quantum gravity spheres as matings of finite-diameter trees (2015) (52)
Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations (2011) (50)
Duality and the Knizhnik-Polyakov-Zamolodchikov relation in Liouville quantum gravity. (2009) (49)
Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula (2012) (49)
Internal DLA in Higher Dimensions (2010) (49)
Imaginary geometry III: reversibility of SLE_\kappa\ for \kappa \in (4,8) (2012) (47)
Random-Turn Hex and Other Selection Games (2005) (44)
Dimers, tilings and trees (2003) (44)
Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition (2011) (40)
Hausdorff Dimension of the SLE Curve Intersected with the Real Line (2007) (38)
CLE PERCOLATIONS (2016) (37)
Large deviations of Markov chains indexed by random trees (2005) (37)
Basic properties of the natural parametrization for the Schramm-Loewner evolution (2009) (35)
Schramm-Loewner evolution and Liouville quantum gravity. (2010) (33)
Equivalence of Liouville measure and Gaussian free field (2014) (29)
Imaginary geometry II: Reversibility of $\operatorname{SLE}_{\kappa}(\rho_{1};\rho_{2})$ for $\kappa\in(0,4)$ (2016) (29)
Delocalization of Uniform Graph Homomorphisms from Z 2 to Z (2018) (28)
Duality and KPZ in Liouville Quantum Gravity (2009) (28)
Random Surfaces: Large Deviations Principles and Gradient Gibbs Measure Classifications (2003) (28)
Harmonic functions on mated-CRT maps (2018) (26)
Ribbon tilings and multidimensional height functions (2001) (25)
Non-simple SLE curves are not determined by their range (2016) (25)
The covariant measure of SLE on the boundary (2008) (22)
Liouville quantum gravity and the Brownian map I: the $$\mathrm{QLE}(8/3,0)$$QLE(8/3,0) metric (2019) (22)
The Tutte Embedding of the Poisson–Voronoi Tessellation of the Brownian Disk Converges to $$\sqrt{8/3}$$-Liouville Quantum Gravity (2018) (22)
Absolutely minimal Lipschitz extension of tree-valued mappings (2010) (20)
Simple conformal loop ensembles on Liouville quantum gravity (2020) (20)
Schramm’s proof of Watts’ formula (2010) (19)
Power law Pólya’s urn and fractional Brownian motion (2009) (17)
Six-vertex model and Schramm-Loewner evolution. (2016) (17)
Imaginary geometry II: reversibility of SLE_\kappa(\rho_1;\rho_2) for \kappa \in (0,4) (2012) (16)
Strong path convergence from Loewner driving function convergence (2010) (15)
Internal DLA for cylinders (2013) (15)
Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces (2020) (15)
Field-measure correspondence in Liouville quantum gravity almost surely commutes with all conformal maps simultaneously (2016) (15)
Conformal Loop Ensembles: The Markovian Characterization (2010) (14)
Conformal Loop Ensembles: Construction via Loop-soups (2010) (13)
Deterministic approximations of random reflectors (2012) (12)
Simple CLE in doubly connected domains (2014) (11)
Delocalization of Uniform Graph Homomorphisms from $${\mathbb {Z}}^2$$ to $${\mathbb {Z}}$$ (2018) (11)
Gaussian free field light cones and SLE κ ( ρ ) (2016) (10)
Geodesics and metric ball boundaries in Liouville quantum gravity (2020) (9)
Brownian loops and the central charge of a Liouville random surface (2020) (9)
Scaling limits of the Schelling model (2018) (8)
BIPOLAR ORIENTATIONS ON PLANAR MAPS AND SLE (2018) (8)
An invariance principle for ergodic scale-free random environments (2018) (8)
Tricolor percolation and random paths in 3D (2013) (7)
Uniqueness of maximal entropy measure on essential spanning forests (2004) (7)
A large-deviation theorem for tree-indexed Markov chains (2003) (6)
Computing and Sampling Restricted Vertex Degree Subgraphs and Hamiltonian Cycles (2000) (6)
Bipolar orientations on planar maps and $\mathrm{SLE}_{12}$ (2019) (5)
ABSOLUTE CONTINUITY OF GAUSSIAN MEASURES UNDER CERTAIN GAUGE TRANSFORMATIONS (2011) (5)
Liouville quantum gravity and the Gaussian free field (2014) (5)
What is a random surface? (2022) (5)
Imaginary geometry II: Reversibility of SLE[subscript κ](ρ[subscript 1];ρ[subscript 2]) for κ ∈ (0,4) (2016) (4)
Strong path convergence from Loewner driving convergence (2010) (4)
Chapter Eight. Internal DLA for Cylinders (2014) (4)
Fixation for distributed clustering processes (2009) (3)
A crude policy whose time has passed (2014) (3)
A duality principle for selection games (2011) (2)
Linear Speed Large Deviations for Percolation Clusters (2003) (2)
Large deviations for random hives and the spectrum of the sum of two random matrices (2021) (1)
2 1 D ec 2 01 0 Schramm-Loewner Evolution and Liouville Quantum Gravity (1)
Best and worst policy control in low-prevalence SEIR (2020) (1)
Gaussian free field light cones and $\mathrm{SLE}_{\kappa }(\rho )$ (2019) (1)
Large deviations for the 3D dimer model (2023) (1)
Beyond the Imperial Frontier: the contest for colonial New Zealand (2016) (1)
Random Variables and Distributions (2008) (1)
Brownian loops on non-smooth surfaces and the Polyakov-Alvarez formula (2023) (1)
A Particle System with Interlacing Pattern SPUR Final Paper, Summer 2013 (2013) (0)
CLE percolations; Arxiv (2016) (0)
Scaling limits of the Schelling model (2019) (0)
The Great War and the Shaping of Indigenous Reponses to the Second World War in Australia, Canada, New Zealand and the United States (2011) (0)
The Tutte Embedding of the Poisson–Voronoi Tessellation of the Brownian Disk Converges to 8/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6 (2019) (0)
A P ] 2 8 A pr 2 00 6 Tug-of-war and the infinity Laplacian (2005) (0)
Ju n 20 09 Fixation for Distributed Clustering Processes (2009) (0)
Absolutely minimal Lipschitz extension of tree-valued mappings (2011) (0)
Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces (2021) (0)
Logarithmic Fluctuations for Internal DLA Citation (2011) (0)
Wilson loop expectations as sums over surfaces on the plane (2023) (0)
Liouville quantum gravity and the Brownian map III: the conformal structure is determined (2021) (0)
18.440 Probability and Random Variables, Spring 2011 (2011) (0)
PR ] 2 D ec 2 01 0 Liouville Quantum Gravity and KPZ (2010) (0)
Tricolor Percolation: is there a 3D SLE_6? (2013) (0)
ec 2 00 3 Gaussian free fields for mathematicians (2003) (0)
Gaussian free field light cones and SLE$_\kappa(\rho)$ (2016) (0)
PR ] 1 0 Ju l 2 01 1 Power law Pólya ’ s urn and fractional Brownian motion (2011) (0)
A contour line of the continuum Gaussian free field (2012) (0)
Imaginary geometry I: interacting SLEs (2016) (0)
Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees (2017) (0)
s urn and fractional Brownian motion (2011) (0)
0 Ju l 2 01 1 Power law Pólya ’ s urn and fractional Brownian motion (2011) (0)
Union Station Lobby at Minute Maid Park (2015) (0)
PR ] 1 9 Ja n 20 10 Fixation for Distributed Clustering Processes (2013) (0)
Power law Pólya’s urn and fractional Brownian motion (2012) (0)
Book Reviews (2010) (0)
Liouville quantum gravity and the Brownian map I: the QLE(8/3,0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathr (2019) (0)
A brief history of internal DLA fluctuation bounds (2013) (0)
Renormalization of Critical Gaussian Multiplicative Chaos and KPZ Relation (2014) (0)

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