Jian Ding's Home Page (丁剑的个人主页)

I am a professor at School of Mathematical Sciences, Peking University. My email address is: d i n g j i a n -at- m a t h -dot- p k u -dot- e d u - dot - c n

I am a member of ProbabilityGroup@PKU. See conferences for group activities, including an International Conference on Probability Theory and Stochastic Analysis in celebration of 110 anniversary of Mathematical Sciences at Peking University.

My research interests are probability theory with focus on interactions with statistical physics, theory of computer science and statistical inference: random walks, Gaussian processes, random constraint satisfaction problems, random planar geometry, spin models, random Schrodinger operators, network recovery problems, etc.

Curriculum Vitae

pdf.

Papers (in reversed chronological order)

A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation (with Z. Li), submitted.
On the prevalence of the periodicity of maximizing measures (with Z. Li and Y. Zhang), submitted.
A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlation (with Z. Li), submitted.
A polynomial-time approximation scheme for the maximal overlap of two independent Erdős-Rényi graphs (with H. Du and S. Gong), submitted.
Long range order for three-dimensional random field Ising model throughout the entire low temperature regime (with Y. Liu and A. Xia), submitted.
Shotgun threshold for sparse Erdős-Rényi graphs (with Y. Jiang and H. Ma), submitted.
Matching recovery threshold for correlated random graphs (with H. Du), submitted.
Shotgun assembly threshold for lattice labeling model (with H. Liu), Probability Theory and Related Fields, published online April 2023.
Detection threshold for correlated Erdős-Rényi graphs via densest subgraphs (with H. Du), IEEE Transactions on Information Theory, published online 2023.
Long range order for random field Ising and Potts models (with Z. Zhuang), accepted by Communications on Pure and Applied Mathematics.
Uniqueness of the critical and supercritical Liouville quantum gravity metrics (with E. Gwynne ), Proceedings of London Mathematical Society, (3) 126 (2023), no. 1, 216–333.
Introduction to the Liouville quantum gravity metric (with J. Dubedat and E. Gwynne ), submitted to ICM proceeding.
The critical Liouville quantum gravity metric induces the Euclidean topology (with E. Gwynne ), submitted.
Up-to-constants comparison of Liouville first passage percolation and Liouville quantum gravity (with E. Gwynne ), Science China Mathematics, 66 (2023), no. 5, 1053–1072.
A New Correlation Inequality for Ising Models with External Fields (with J. Song and R. Sun ), Probability Theory and Related Fields, published online April 2022.
Regularity and confluence of geodesics for the supercritical Liouville quantum gravity metric (with E. Gwynne ), submitted.
The planted matching problem: Sharp threshold and infinite-order phase transition (with Y. Wu, J. Xu and D. Yang ), Probability Theory and Related Fields, published online 2023.
Correlation length of two-dimensional random field Ising model via greedy lattice animal, (with M. Wirth) Duke Math Journal, published online 2023.
Distances in critical long range percolation (with A. Sly ), submitted.
Proof of the satisfiability conjecture for large $k$ (with A. Sly and N. Sun ), Conference version at STOC 2015, Journal version in Annals of Mathematics (2), 196 (2022), no. 1, 1–388.
The distance exponent for Liouville first passage percolation is positive (with E. Gwynne and A. Sepulveda), Probability theory and related fields, 181: 1035–1051 (2021).
Crossing estimates from metric graph and discrete GFF, (with M. Wirth and H. Wu ) Annales de l' Institut Henri Poincare, 58 (3) 1740 - 1774, August 2022.
Tightness of supercritical Liouville first passage percolation (with E. Gwynne ), Journal of European Mathematical Society, to appear.
Supercritical minimum mean-weight cycles (with N. Sun and D. Wilson ), Transactions in AMS, to appear.
Consistent recovery threshold of hidden nearest neighbor graphs (with Y. Wu, J. Xu and D. Yang ), Conference version at COLT 2020, Journal version at IEEE Transactions on Information Theory, 67 (8): 5211--5229 (2021).
Exponential decay of correlations in the two-dimensional random field Ising model (with J. Xia ), Inventiones, Volume 224, 999--1045 (2021).
Efficient random graph matching via degree profiles (with Z. Ma, Y. Wu and J. Xu ), Probability theory and related fields, Volume 179, 29--115 (2021).
Distribution of the random walk conditioned on survival among quenched Bernoulli obstacles (with R. Fukushima , R. Sun and C. Xu ), Annals of Probability, 49(1): 206-243 (2021).
Tightness of Liouville first passage percolation for $\gamma \in (0, 2)$ (with J. Dubedat, A. Dunlap and H. Falconet ), Publ. Math. IHES, 132: 353--403(2020).
Biased random walk conditioned on survival among Bernoulli obstacles: subcritical phase (with R. Fukushima , R. Sun and C. Xu ), Communications in Mathematical Physics, Volume 376, 2161--2195 (2020).
Geometry of the random walk range conditioned on survival among Bernoulli obstacles (with R. Fukushima , R. Sun and C. Xu ), Probability Theory and Related Fields, 177: 91--145 (2020).
Percolation for level-sets of Gaussian free fields on metric graphs, (with M. Wirth ) Annals of Probability, 48 (3): 1411--1435, 2020.
Subsequential scaling limits for Liouville graph distance, (with A. Dunlap ) Communications in Mathematical Physics, Volume 376, 1499--1572 (2020).
Localization for random walks among random obstacles in a single Euclidean ball (with C. Xu ), Communications in Mathematical Physics, Volume 375, 949--1001(2020).
The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds (with E. Gwynne ), Communications in Mathematical Physics, Volume 219, 467--506 (2020).
Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field, (with M. Biskup and S. Goswami ) Communications in Mathematical Physics, Volume 373, 45--106 (2020).
Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice (with C. Smart ), Inventiones, Volume 219, 467--506 (2020).
Hidden Hamiltonian Cycle Recovery via Linear Programming (with V. Bagaria, D. Tse, Y. Wu and J. Xu ), Operations Research, Volume 68, Issue 1, 2020.
Heat kernel for Liouville Brownian motion and Liouville graph distance (with O. Zeitouni and F. Zhang ), Communications in Mathematical Physics, Volume 371, 561--618 (2019).
Capacity lower bound for the Ising perceptron (with N. Sun ), STOC 2019.
Cut-off for lamplighter chains on tori: dimension interpolation and phase transition, (with A. Dembo, J. Miller and Y. Peres ) Probability Theory and Related Fields, Volume 173, Issue 1-2, pp 605--650, 2019.
Upper bounds on Liouville first-passage percolation and Watabiki's prediction, (with S. Goswami ) Communications on Pure and Applied Mathematics, Volume 72, Issue 11, 2331--2384 2019.
When Multiplicative Noise Stymies Control, (with Y. Peres, G. Ranade and A. Zhai ) Annals of Applied Probability, Volume 29, Number 4 (2019), 1963--1992.
Poly-logarithmic localization for random walks among random obstacles (with C. Xu ), Annals of Probability, Volume 47, Number 4 (2019), 2011--2048.
Liouville first passage percolation: geodesic length exponent is strictly larger than 1 at high temperatures, (with F. Zhang ) Probability Theory and Related Fields, Volume 174 (2019), Issue 1--2.
Continuous Monitoring of $\ell_p$ Norms in Data Streams (with J. Blasiok and J. Nelson ), APPROX/RANDOM 2017.
On the Liouville heat kernel for $k$-coarse MBRW (with O. Zeitouni and F. Zhang ), Electronic Journal of Probability, 23 (2018), no. 62, 20 pp.
Three favorite sites occurs infinitely often for one-dimensional simple random walk, (with J. Shen ) Annals of Probability, Volume 46, Number 5 (2018), 2545--2561.
Chemical distances for percolation of planar Gaussian free fields and critical random walk loop soups, (with L. Li ) Communications in Mathematical Physics, 360 (2018), 2: 523--553.
Liouville first-passage percolation: subsequential scaling limit at high temperature, (with A. Dunlap ) Annals of Probability, 47 (2019), no. 2: 690--742.
First passage percolation on the exponential of two-dimensional branching random walk, (with S. Goswami ) Electronic Communication in Probability, 22 (2017), no. 69, 14 pp.
Non-universality for first passage percolation on the exponential of log-correlated Gaussian fields, (with F. Zhang ) Probability Theory and Related Fields, 171 (2018), no. 3--4, 1157--1188.
Convergence of the centered maximum of log-correlated Gaussian fields (with R. Roy and O. Zeitouni ), Annals of Probability, 45 (2017), no. 6A, 3886--3928.
Convergence in law of the maximum of nonlattice branching random walk (with M. Bramson and O. Zeitouni ), Annales de l' Institut Henri Poincare, Volume 52, Number 4 (2016), 1897--1924.
Maximum independent sets on random regular graphs (with A. Sly and N. Sun ), Acta Mathematica , 217 (2016), 2:263--340.
Percolation of averages in the stochastic mean field model: the near-supercritical regime, (with S. Goswami ) Electronic Journal of Probability, 20(2015), no.124, 1-21.
Testing for high-dimensional geometry in random graphs (with S. Bubeck, R. Eldan and M Racz), Random Structures and Algorithms, 49 (2016), 3: 503--532.
Satisfiability threshold for random regular NAE-SAT (with A. Sly and N. Sun ), Conference version at STOC 2014, Journal version at Communications in Mathematical Physics , 341(2016), 2: 435-489.
Convergence in law of the maximum of the two-dimensional discrete Gaussian free field (with M. Bramson and O. Zeitouni ), Communications on Pure and Applied Mathematics, 69(2016), 1:62-123 .
On multiple peaks and moderate deviations for the supremum of a Gaussian field (with R. Eldan and A. Zhai ), Annals of Probability, 43(2015), 6:3468--3493.
Bandits with Switching Costs: $T^{2/3}$ Regret, (with O. Dekel, T. Koren and Y. Peres ) STOC(2014), 459--467.
Mixing under monotone censoring , (with E. Mossel ) Electronic Communications in Probability , 19(2014), no. 46, 1--6.
Extreme values for two-dimensional discrete Gaussian free field (with O. Zeitouni ), Annals of Probability, 42(2014), 1480--1515.
Asymptotics of cover times via Gaussian free fields: bounded-degree graphs and general trees , Annals of Probability, 2014, 42(2), 464--496.
Sensitivity of mixing times , (with Y. Peres ) Electronic Communications in Probability , 18 (2013), no. 88, 1--6.
Markov type and threshold embeddings (with J. Lee and Y. Peres ), Geometric and Functional Analysis , Volume 23 (2013), Issue 4,1207-1229.
Persistence of iterated partial sums , (with A. Dembo and F. Gao) Annales de l' Institut Henri Poincare, Volume 49, Number 3 (2013), 873--884.
Glauber Dynamics for the mean-field Potts Model, (with P. Cuff, O. Louidor, E. Lubetzky, Y. Peres and A. Sly ) Journal of Statistical Physics, 149(3):432-477, November, 2012.
Anatomy of the giant component: The strictly supercritical regime , (with E. Lubetzky and Y. Peres ) European Journal of Combinatorics , Volume 35(2014), 155-168.
Scaling window for mean-field percolation of averages , Annals of Probability, Volume 41, Number 6 (2013), 3697-4427.
On cover times for 2D lattices , Electronic Journal of Probability, 17 (2012), no. 45, 1-18.
Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field , Probability Theory and Related Fields, Volume 157, Issue 1-2 (2013), 285--299.
A sharp estimate for cover times on binary trees (with O. Zeitouni ), Stochastic Processes and Applications, 122(5): 2117 - 2133 (2012).
The Hitchhiker's Guide to Affiliation Networks: A Game-Theoretic Approach (with C. Borgs , J. Chayes and B. Lucier ), ICS (2011) .
Cover times, blanket times, and majorizing measures , (with J. Lee and Y. Peres ), journal version at Annals of Math 175(3) : 1409-1471 (2012), conference version at STOC (2011).
The evolution of the cover time (with M. Barlow , A. Nachmias and Y. Peres ), Combinatorics, Probability and Computing, 20(3): 331-345 (2011).
Mixing time for the Ising model: a uniform lower bound for all graphs , (with Y. Peres ), Annales de l' Institut Henri Poincare, 47(4): 1020-1028 (2011)..
Mixing time of near-critical random graphs , (with E. Lubetzky and Y. Peres ), Annals of Probability, 40 (3): 979-1008 (2012).
Diameters in supercritical random graphs via first passage percolation (with J.H. Kim , E. Lubetzky and Y. Peres ), Combinatorics, Probability and Computing, 19 (5-6): 729-751 (2010).
Anatomy of a young giant component in the random graph (with J.H. Kim , E. Lubetzky and Y. Peres ), Random Structures and Algorithms, 39(2): 139-178 (2011).
Mixing time of critical Ising model on trees is polynomial in the height (with E. Lubetzky and Y. Peres ), Communications in Mathematical Physics, 295 (2010), no. 1, 161-207.
Censored Glauber Dynamics for the mean field Ising Model (with E. Lubetzky and Y. Peres ), Journal of Statistical Physics 137 (2009), no. 3, 407-458.
The mixing time evolution of Glauber dynamics for the mean-field Ising model (with E. Lubetzky and Y. Peres ), Communications in Mathematical Physics, Volume 289, Number 2, July, 2009.
Total-variation cutoff in birth-and-death chains (with E. Lubetzky and Y. Peres ), Probability Theory and Related Fields, 146 (2010), no. 1, 61-85.

Students and Postdocs

Zijie Zhuang, current student, University of Pennsylvania.
Linjun Li, Ph.D. 2022, University of Pennsylvania. Now works in financial industry.
Jiaming Xia, Ph.D. 2022, University of Pennsylvania (jointly supervised with Robin Pemantle). Now postdoc at IHES.
Mateo Wirth, Ph.D. 2021, University of Pennsylvania, now at Facebook.
Changji Xu , Ph.D. 2020 at University of Chicago, now postdoc at Harvard.
Jianfei Shen: Master 2017 at University of Chicago, now at Alibaba.
Li Li: Ph.D 2017 at University of Chicago.
Subhajit Goswami: Ph.D 2017 at University of Chicago, now assistant professor at TIFR.
Rishideep Roy: Ph.D 2016 at University of Chicago, now assistant professor at IIM Bangalore.
Fan Yang: postdoc 2019-2022, University of Pennsylvania. Now associate professor at Tsinghua.

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