Antonio Auffinger
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Antonio Auffinger has a total of 14 co-authors. Here are the top co-authors by number of shared publications:
- Qiang Zeng
Department of Mathematics University of Macau
5 shared publications - Wei-Kuo Chen
University of Minnesota, Minneapolis, USA
4 shared publications - Aukosh Jagannath
Harvard University
2 shared publications - Si Tang
Lehigh University
2 shared publications - Si Tang
Northwestern University University of Chicago
2 shared publications - Cathy Xi Chen
Department of Mathematics, Northwestern University, Evanston, USA
1 shared publication
Latest Publications
- Open Access
- 20 November 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (12) , 314
The Spherical $p+s$ Spin Glass at Zero TemperatureWe determine the structure of the Parisi measure at zero temperature for the spherical $$p+s$$ 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.- 20 November 2025
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 406 (12) , 314
Open AccessThe Spherical $p+s$ Spin Glass at Zero TemperatureWe determine the structure of the Parisi measure at zero temperature for the spherical $$p+s$$ 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. - Open Access
On the time constant of high dimensional first passage percolation, revisited
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.Open AccessOn the time constant of high dimensional first passage percolation, revisited
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. - Open Access
- 1 January 2025
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 30 (none) , 1-13
On the time constant of high dimensional first passage percolation, revisited
In [2], it was claimed that the time constant μd(e1) for the first-passage percolation model on Zd is μd(e1)∼logd∕(2ad) as d→∞, if the passage times (τe)e∈Ed are i.i.d., with a common c.d.f. F satisfying F(x) x−a≤C |logx| for some constants a,C and sufficiently small x. However, the proof of the upper bound, namely, Equation (2.1) in [2] lim supd→∞μd(e1)ad logd≤1 2(0.1) is incorrect. In this article, we provide a different approach that establishes (0.1). 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((logd∕d)2) as d→∞ in the case of the when the edge weights are exponentially distributed.
- 1 January 2025
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 30 (none) , 1-13
Open AccessOn the time constant of high dimensional first passage percolation, revisited
In [2], it was claimed that the time constant μd(e1) for the first-passage percolation model on Zd is μd(e1)∼logd∕(2ad) as d→∞, if the passage times (τe)e∈Ed are i.i.d., with a common c.d.f. F satisfying F(x) x−a≤C |logx| for some constants a,C and sufficiently small x. However, the proof of the upper bound, namely, Equation (2.1) in [2] lim supd→∞μd(e1)ad logd≤1 2(0.1) is incorrect. In this article, we provide a different approach that establishes (0.1). 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((logd∕d)2) as d→∞ in the case of the when the edge weights are exponentially distributed.
- 1 July 2023
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 402 (1) , 951-993
Complexity of Gaussian Random Fields with Isotropic Increments
- 1 July 2023
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 402 (1) , 951-993
Complexity of Gaussian Random Fields with Isotropic Increments
- Open Access
Equilibrium Distributions for t-distributed Stochastic Neighbour Embedding
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.
Open AccessEquilibrium Distributions for t-distributed Stochastic Neighbour Embedding
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.
- 2 March 2023
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 186 (1-2) , 285-326
Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups
- 2 March 2023
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 186 (1-2) , 285-326
Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups
- Open Access
Complexity of Gaussian random fields with isotropic increments
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a Gaussian process with isotropic increments. We derive asymptotic formulas for the mean number of critical points with critical values in an open set as the dimension $N$ goes to infinity. In a companion paper, we provide the same analysis for the number of critical points with a given index.Open AccessComplexity of Gaussian random fields with isotropic increments
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a Gaussian process with isotropic increments. We derive asymptotic formulas for the mean number of critical points with critical values in an open set as the dimension $N$ goes to infinity. In a companion paper, we provide the same analysis for the number of critical points with a given index. - 1 April 2022
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 63 (4) , 043303
Sharp complexity asymptotics and topological trivialization for the (p, k) spiked tensor model
Using precise random matrix theory tools and the Kac–Rice formula, we provide sharp O(1) asymptotics for the average number of deep minima of the (p, k) spiked tensor model. These sharp estimates allow us to prove that, when the signal-to-noise ratio is large enough, the expected number of deep minima is asymptotically finite as N tends to infinity and to establish the occurrence of topological trivialization by showing that this number vanishes when the strength of the signal-to-noise ratio diverges. We also derive an explicit formula for the value of the absolute minimum (the limiting ground state energy) on the N-dimensional sphere, similar to the recent work of Jagannath, Lopatto, and Miolane [Ann. Appl. Probab. 4, 1910–1933 (2020)].
- 1 April 2022
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 63 (4) , 043303
Sharp complexity asymptotics and topological trivialization for the (p, k) spiked tensor model
Using precise random matrix theory tools and the Kac–Rice formula, we provide sharp O(1) asymptotics for the average number of deep minima of the (p, k) spiked tensor model. These sharp estimates allow us to prove that, when the signal-to-noise ratio is large enough, the expected number of deep minima is asymptotically finite as N tends to infinity and to establish the occurrence of topological trivialization by showing that this number vanishes when the strength of the signal-to-noise ratio diverges. We also derive an explicit formula for the value of the absolute minimum (the limiting ground state energy) on the N-dimensional sphere, similar to the recent work of Jagannath, Lopatto, and Miolane [Ann. Appl. Probab. 4, 1910–1933 (2020)].
- 13 August 2021
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 184 (2) , 1-25
Thouless–Anderson–Palmer Equations for the Ghatak–Sherrington Mean Field Spin Glass Model
- 13 August 2021
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 184 (2) , 1-25
Thouless–Anderson–Palmer Equations for the Ghatak–Sherrington Mean Field Spin Glass Model
- Open Access
The SK model is infinite step replica symmetry breaking at zero temperature
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.
Open AccessThe SK model is infinite step replica symmetry breaking at zero temperature
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.