40.Equilibrium Distributions for t-distributed Stochastic Neighbour Embedding.
Antonio Auffinger, Daniel Fletcher. Preprint.
Graduate students and post-docs mentored
Julian Gold - NSF Postdoc, 2017-2021
Qiang Zeng - Boas Assistant Professor, 2016-2018
Zhehua Li - Posdoctoral Lecturer, 2019-2021
Cathy Chen - Ph.D. 2022
Daniel Fletcher - Graduate student
Christian Gorski - Graduate student
Curtis Grant - Graduate student
Yi Gu - Graduate student
Pax Kivimae - Ph.D. 2022
Si Tang - Ph.D. 2017
Yuxin Zhou - Graduate student
Papers and preprints
Research currently sponsored by NSF grants DMS #2154076, NSF CAREER grant DMS #1653552 and by Simons Foundation/SFARI (597491-RWC).
39. The spherical p+s spin glass at zero temperature.
Antonio Auffinger, Yuxin Zhou. Preprint.
38. Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups.
Antonio Auffinger, Christian Gorski. Probability Theory and Related Fields (2023) https://doi.org/10.1007/s00440-023-01196-7
37. Optimization of random high-dimensional functions: Structure and algorithms.
Antonio Auffinger, Andrea Montanari, Eliran Subag To appear as a contribution to the edited volume "Spin Glass Theory, Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific.
36. Complexity of Gaussian random fields with isotropic increments: critical points with given indices.
Antonio Auffinger, Qiang Zeng. Preprint.
33. Complexity of high dimensional Gaussian random fields with isotropic increments.
Antonio Auffinger, Qiang Zeng to appear at Comm. Math. Phys.
35. Sharp complexity asymptotics and topological trivialization for the (p, k) spiked tensor model.
Antonio Auffinger, Gerard Ben Arous, Zhehua Li Journal of Mathematical Physics, Volume 63, Issue 4 - special collection in honor of Freeman Dyson.
34. Thouless-Anderson-Palmer equations for the Ghatak-Sherrington mean field spin glass model.
Antonio Auffinger, Cathy Xi Chen Journal of Statistical Physics volume 184, Article number: 22 (2021)
32. The number of saddles of the spherical p-spin model.
Antonio Auffinger, Julian Gold. Preprint.
31. On properties of the spherical mixed vector p-spin model.
Antonio Auffinger, Yuxin Zhou. Stochastic Processes and their Applications Volume 146, April 2022, Pages 382-413.
30. Topologies of random geometric complexes on Riemannian manifolds in the thermodynamic limit.
Antonio Auffinger, Antonio Lerario, Erik Lundberg. IMRN Volume 2021, Issue 20, October 2021, Pages 15497–15532.
29. On spin distributions for generic p-spin models.
Antonio Auffinger, Aukosh Jagannath. J. Stat. Phys, Volume 174, 316--332, (2019).
28. Existence of two-step replica symmetry breaking for the spherical mixed spin glass at zero temperature.
Antonio Auffinger, Qiang Zeng. Comm. Math. Phys., Volume 370, Issue 1, pp 377--402, (2019)
27. Pemantle's min-plus binary tree.
Antonio Auffinger, Dylan Cable. Preprint.
26. The SK model is Full-Step Replica Symmetry Breaking at zero temperature.
Antonio Auffinger, Wei-Kuo Chen, Qiang Zeng. Comm. Pure Appl. Math., 73: 921-943, (2020)
25. On the energy landscape of the spherical p-spin model.
Antonio Auffinger, Wei-Kuo Chen. Advances in Mathematics 330 (2018), 553–588.
24. Thouless-Palmer-Anderson equations for conditional Gibbs measures in the generic p-spin glass model.
Antonio Auffinger, Aukosh Jagannath. Annals of Probability, Volume 47, Number 4 (2019), 2230-2256
23. On concentration properties of disordered Hamiltonians.
Antonio Auffinger, Wei-Kuo Chen. Proceedings of the AMS. 146, 1807-1815 (2018).
22. Parisi formula for the ground state energy in the mixed p-spin model.
Antonio Auffinger, Wei-Kuo Chen. Annals of Probability 2017, Vol. 45, No. 6B, 4617-4631.
21. A duality principle in spin glasses.
Antonio Auffinger, Wei-Kuo Chen. Electron. J. Probab., Volume 22 (2017), paper no. 61, 17 pp.
20. 50 years of First Passage Percolation.
Antonio Auffinger, Michael Damron and Jack T. Hanson. University Lecture Series, Vol. 68; 2017; 161pp.
19. The Legendre structure of the Parisi formula.
Antonio Auffinger and Wei-Kuo Chen. Comm. Math. Phys. Vol. 348, Issue 3, pp 751–770, (2016).
18. Extreme eigenvalues of sparse, heavy tailed random matrices.
Antonio Auffinger and Si Tang. Stochastic Processes and Applications, Vol. 126, Issue 11, November 2016, Pages 3310-3330.
17. Universality of chaos and ultrametricity in mixed p-spin models.
Antonio Auffinger and Wei-Kuo Chen. Comm. on Pure and Applied Math. Vol. LXIX, 2107–2130 (2016)
16. On the time constant of high dimensional first-passage percolation.
Antonio Auffinger and Si Tang. Electron. J. Probab. Volume 21 (2016), paper no. 24, 23 pp
15. Rate of convergence of the mean for sub-additive ergodic sequences.
Antonio Auffinger, Michael Damron and Jack T. Hanson. Advances in Mathematics, Volume 285, 5 November 2015, Pages 138-181
14. The Parisi formula has a unique minimizer.
Antonio Auffinger, Wei-Kuo Chen. Comm. Math. Phys. 2015, Vol. 335, Issue 3, pp 1429-1444
13. A simplified proof of the relation between scaling exponents in first-passage percolation.
Antonio Auffinger, Michael Damron. Annals of Probability 42 (2014), no. 3, 1197–1211
12. Upper and lower bounds for stochastic processes.
Antonio Auffinger. Bull. Amer. Math. Soc. (N.S.) 53 (2016), no. 1, 173–177
11. On properties of Parisi measures.
Antonio Auffinger, Wei-Kuo Chen. Probab. Theory and Rel. Fields. 2015, Vol. 161, Issue 3, pp 817-850.
10. Free energy and complexity of spherical bipartite models.
Antonio Auffinger, Wei-Kuo Chen. J. Stat. Phys. 2014, Volume 157, Issue 1, pp 40-59
9. Limiting geodesic for first-passage percolation on subsets of Z^2.
Antonio Auffinger, Michael Damron, Jack T. Hanson. Ann. Appl. Probab. 2015, Vol. 25, No. 1, 373-405.
8. The scaling relation chi = 2 xi -1 for directed polymers in a random environment.
Antonio Auffinger, Michael Damron. ALEA, Lat. Am. J. Probab. Math. Stat. 10 (2), 857-880 (2013)
7. Complexity of random functions of many variables.
Antonio Auffinger, Gerard Ben Arous. Annals of Probability 2013, Vol. 41, No. 6, 4214-4247
6. Differentiability at the edge of the percolation cone and related results in first-passage percolation.
Antonio Auffinger, Michael Damron. Probab. Theory Related Fields, 2013 Volume 156, Issue 1-2, pp 193-227
5. Random Matrices and Complexity of Spherical Spin Glasses.
Antonio Auffinger, Gerard Ben Arous, Jiri Cerny. Comm. on Pure and Applied Math. Volume 66, Issue 2 (2013)
4. Directed polymers in random environment with heavy tails.
Antonio Auffinger, Oren Louidor. Comm. on Pure and Applied Math. Volume 64 no. 2, 183-204 (2011)
3. Poisson convergence for the largest eigenvalues of heavy tailed random matrices.
Antonio Auffinger, Gerard Ben Arous, Sandrine Peche. Annales de l'Institut Henri Poincare Volume 45 no. 3 pg. 589-610 (2009)
2. Random matrices, complexity of spin glasses and heavy tailed processes.
Antonio Auffinger. New York University New York, NY, USA, ISBN: 978-1-124-80735-5
1. Universality for directed polymers in thin rectangles.
Antonio Auffinger, Jinho Baik, Ivan Corwin.
Recent conferences that I organized:
SPA 2019 - July 8th-12th, 2019, at Northwestern, co-organized with Jian Ding, Elton Hsu and Greg Lawler.40th Midwest Probability Colloquim - October 8th-10th, 2018 , at Northwestern, co-organized with Elton Hsu.
Spin glasses and related topics - September 30th-October 5th, 2018, at BIRS, Banff co-organized with Wei-Kuo Chen, Dmitry Panchenko and Lenka Zdeborova.
2nd Northwestern Summer school in Probability - July 16th-25th, 2018 , at Northwestern, co-organized with Elton Hsu.
SNAP 2017 - July 24th-August 11th, 2017, at Northwestern, co-organized with Laura DeMarco, Ezra Getzler, Aaron Naber, Aaron Peterson, Valentino Tosatti, Ben Weinkove, Jared Wunsch.
Dynamics, aging and universality in complex systems - June 2017, Courant Institute, New York, NY, co-organized with Paul Bourgade, Ivan Corwin and Alice Guionnet.
Session on spin glasses and disordered media at the 2017 Joint Mathematics Meeting - January 2017, Atlanta, co-organized with Aukosh Jagannath and Dmitry Panchenko.
Northwestern Summer school in Probability - July 11th-22nd, 2016 , at Northwestern, co-organized with Elton Hsu.
Emphasis Year in Probability - 2015/2016, at Northwestern, co-organized with Elton Hsu and Steve Zelditch.
Workshop on percolation, spin glasses and random media - May 26th-29th, 2016, at Northwestern, co-organized with Elton Hsu.
Workshop in first passage percolation and related models - August, 2015, at AIM, co-organized with Michael Damron and Jack Hanson.