About

Antonio Auffinger is a professor at Northwestern University's Department of Mathematics, specializing in probability theory with a focus on spin glasses, first passage percolation, and random matrices. He is actively involved in research supported by NSF grants and the Simons Foundation, contributing to the understanding of complex stochastic processes and high-dimensional random functions. Auffinger serves as an associate editor for prominent journals including the Annals of Probability, Bulletin of the AMS, and the Journal of Statistical Physics. His work encompasses the study of replica symmetry breaking, energy landscapes in spin glass models, and the complexity of Gaussian random fields, reflecting a deep engagement with both theoretical and applied aspects of probability and statistical physics. Additionally, he has played a significant role in organizing conferences and workshops that advance research in random dynamical systems, spin glass theory, and related probabilistic models.

Research topics

• Mathematics
• Computer Science
• Thermodynamics
• Physics
• Combinatorics
• Linguistics
• Philosophy
• Classical mechanics
• Library science
• Geometry
• Condensed matter physics
• Statistical physics

Selected publications

• On the time constant of high dimensional first passage percolation, revisited

  Electronic Journal of Probability · 2025-01-01

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• The Spherical $$p+s$$ Spin Glass at Zero Temperature

  Communications in Mathematical Physics · 2025-11-20

  articleOpen access1st authorCorresponding

  Abstract We determine the structure of the Parisi measure at zero temperature for the spherical $$p+s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> spin glass model. We show that depending on the values of p and s , four scenarios may emerge, including the existence of 1-FRSB and 2-FRSB phases as predicted by Crisanti and Leuzzi (Private communication, 2022, Phys Rev B 73:014412, 2006). We also provide consequences for the model at low temperatures.

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• On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses

  ArXiv.org · 2025-06-02

  preprintOpen access1st authorCorresponding

  We show that in mean-field spin glasses, a discontinuous breaking of replica symmetry at the critical inverse temperature $β_c$ implies the existence of an intermediate shattered phase. This confirms a prediction from physics regarding the nature of random first order phase transitions. On the other hand, we give an example of a spherical spin glass which exhibits shattering, yet the transition is continuous at $β_c$.

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• On the time constant of high dimensional first passage percolation, revisited

  ArXiv.org · 2025-01-20

  preprintOpen access1st authorCorresponding

  In [2], it was claimed that the time constant $μ_{d}(e_{1})$ for the first-passage percolation model on $\mathbb Z^{d}$ is $μ_{d}(e_{1}) \sim \log d/(2ad)$ as $d\to \infty$, if the passage times $(τ_{e})_{e\in \mathbb E^{d}}$ are i.i.d., with a common c.d.f. $F$ satisfying $\left|\frac{F(x)}{x}-a\right| \le \frac{C}{|\log x|}$ for some constants $a, C$ and sufficiently small $x$. However, the proof of the upper bound, namely, Equation (2.1) in [2] \begin{align} \limsup_{d\to\infty} \frac{μ_{d}(e_{1})ad}{\log d} \le \frac{1}{2} \end{align} is incorrect. In this article, we provide a different approach that establishes this inequality. As a side product of this new method, we also show that the variance of the non-backtracking passage time to the first hyperplane is of order $o\big((\log d/d)^{2}\big)$ as $d\to \infty$ in the case of the when the edge weights are exponentially distributed.

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• Optimization of Random High-Dimensional Functions: Structure and Algorithms

  WORLD SCIENTIFIC eBooks · 2023-08-01 · 8 citations

  book-chapter1st authorCorresponding
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• Complexity of Gaussian Random Fields with Isotropic Increments

  Communications in Mathematical Physics · 2023-07-01 · 7 citations

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• Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups

  Probability Theory and Related Fields · 2023-03-02 · 1 citations

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• Equilibrium Distributions for t-distributed Stochastic Neighbour Embedding

  arXiv (Cornell University) · 2023-04-07 · 1 citations

  preprintOpen access1st authorCorresponding

  We study the empirical measure of the output of the t-distributed stochastic neighbour embedding algorithm when the initial data is given by n independent, identically distributed inputs. We prove that under certain assumptions on the distribution of the inputs, this sequence of measures converges to an equilibrium distribution, which is described as a solution of a variational problem.

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• Optimization of random high-dimensional functions: Structure and algorithms

  arXiv (Cornell University) · 2022-06-21

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  Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated to leaves of a tree, and the Euclidean distance between them corresponds to the distance along this tree. We survey recent progress towards a rigorous proof of this picture in the context of mixed $p$-spin spin glass models. We focus in particular on the following topics: $(i)$~The structure of critical points of the Hamiltonian; $(ii)$~The realization of the ultrametric tree as near optima of a suitable TAP free energy; $(iii)$~The construction of efficient optimization algorithm that exploits this picture.

  PublisherOA PDFDOI

• On properties of the spherical mixed vector p-spin model

  Stochastic Processes and their Applications · 2022-02-09 · 3 citations

  article1st authorCorresponding
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Recent grants

• Complexity of Disordered Systems

  NSF · $110k · 2014–2017

• Complexity of Disordered Systems

  NSF · $144k · 2014–2015

• CAREER: Complexity of Disordered Systems

  NSF · $500k · 2017–2026

Frequent coauthors

• Michael Damron

  21 shared

• Wei-Kuo Chen

  University of Minnesota System

  15 shared

• Gérard Ben Arous

  New York University

  15 shared

• Jack Hanson

  12 shared

• Aukosh Jagannath

  University of Waterloo

  11 shared

• Wei‐Kuo Chen

  11 shared

• Qiang Zeng

  4 shared

• Si Tang

  Lehigh University

  4 shared

Labs

• Antonio Auffinger's LabPI

  Research in mathematics, particularly in the fields of spin glasses, first passage percolation, and random matrices.