Haoran Yang
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Haoran Yang has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Lihu Xu
Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao, China
4 shared publications - Arnaud Guillin
Laboratoire de Mathématiques Blaise Pascal UMR 6620, CNRS, Université Clermont-Auvergne, Aubière, France
2 shared publications - Hao Ge
Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
2 shared publications - Xiang Li
Faculty of Science and Technology, University of Macau, Macau, China
2 shared publications Yu Wang
2 shared publicationsHao Xu
Department of Mathematics University of Macau
1 shared publication
Latest Publications
- 1 September 2025
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 66 (9)
Hessian spectrum at the global minimum of the spherical pure-like mixed p-spin glasses
We study the large N-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed p-spin models. Specifically, we show that its empirical spectral measure converges in probability to a shifted and rescaled semicircle law and does not have outliers. Our method follows the second moment approach developed recently in Arous et al. [Commun. Pure Appl. Math. 73(8), 1732–1828 (2020)], from which the ground state energy can be derived for the pure-like mixed p-spin model. By analyzing the complexity function with given radial derivative and energy, we derive the convergence of the Hessian spectrum from the vanishing mean number of critical points. For the 1-RSB model, the ground state energy was explicitly computed in Huang and Sellke [arXiv:2311.15495 (2023)]. Combined with the complexity function of local maxima with given radial derivative obtained in Belius and Schmidt [arXiv:2207.14361 (2022)], this allows us to obtain the corresponding results more directly. Our result extends those corresponding results in the regime of topology trivialization.
- 1 September 2025
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 66 (9)
Hessian spectrum at the global minimum of the spherical pure-like mixed p-spin glasses
We study the large N-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed p-spin models. Specifically, we show that its empirical spectral measure converges in probability to a shifted and rescaled semicircle law and does not have outliers. Our method follows the second moment approach developed recently in Arous et al. [Commun. Pure Appl. Math. 73(8), 1732–1828 (2020)], from which the ground state energy can be derived for the pure-like mixed p-spin model. By analyzing the complexity function with given radial derivative and energy, we derive the convergence of the Hessian spectrum from the vanishing mean number of critical points. For the 1-RSB model, the ground state energy was explicitly computed in Huang and Sellke [arXiv:2311.15495 (2023)]. Combined with the complexity function of local maxima with given radial derivative obtained in Belius and Schmidt [arXiv:2207.14361 (2022)], this allows us to obtain the corresponding results more directly. Our result extends those corresponding results in the regime of topology trivialization.
- 29 November 2024
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 38 (1) , 1-51
Stable Central Limit Theorem in Total Variation Distance
- 29 November 2024
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 38 (1) , 1-51
Stable Central Limit Theorem in Total Variation Distance
- Open Access
Error estimates between SGD with momentum and underdamped Langevin diffusion
Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped Langevin diffusion. In this paper, we establish a quantitative error estimate between them in the 1-Wasserstein and total variation distances.
Open AccessError estimates between SGD with momentum and underdamped Langevin diffusion
Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped Langevin diffusion. In this paper, we establish a quantitative error estimate between them in the 1-Wasserstein and total variation distances.
- Open Access
ERROR ESTIMATES BETWEEN SGD WITH MOMENTUM AND UNDERDAMPED LANGEVIN DIFFUSION
Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped Langevin diffusion. In this paper, we establish a quantitative error estimate between them in the 1-Wasserstein and total variation distances.
Open AccessERROR ESTIMATES BETWEEN SGD WITH MOMENTUM AND UNDERDAMPED LANGEVIN DIFFUSION
Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped Langevin diffusion. In this paper, we establish a quantitative error estimate between them in the 1-Wasserstein and total variation distances.
- Open Access
On the expected number of critical points of locally isotropic Gaussian random fields
We consider locally isotropic Gaussian random fields on the $N$-dimensional Euclidean space for fixed $N$. Using the so called Gaussian Orthogonally Invariant matrices first studied by Mallows in 1961 which include the celebrated Gaussian Orthogonal Ensemble (GOE), we establish the Kac--Rice representation of expected number of critical points of non-isotropic Gaussian fields, complementing the isotropic case obtained by Cheng and Schwartzman in 2018. In the limit $N=\infty$, we show that such a representation can be always given by GOE matrices, as conjectured by Auffinger and Zeng in 2020.Open AccessOn the expected number of critical points of locally isotropic Gaussian random fields
We consider locally isotropic Gaussian random fields on the $N$-dimensional Euclidean space for fixed $N$. Using the so called Gaussian Orthogonally Invariant matrices first studied by Mallows in 1961 which include the celebrated Gaussian Orthogonal Ensemble (GOE), we establish the Kac--Rice representation of expected number of critical points of non-isotropic Gaussian fields, complementing the isotropic case obtained by Cheng and Schwartzman in 2018. In the limit $N=\infty$, we show that such a representation can be always given by GOE matrices, as conjectured by Auffinger and Zeng in 2020. - Open Access
Stable central limit theorem in total variation distance
Under certain general conditions, we prove that the stable central limit theorem holds in the total variation distance and get its optimal convergence rate for all $α\in (0,2)$. Our method is by two measure decompositions, one step estimates, and a very delicate induction with respect to $α$. One measure decomposition is light tailed and borrowed from \cite{BC16}, while the other one is heavy tailed and indispensable for lifting convergence rate for small $α$. The proof is elementary and composed of the ingredients at the postgraduate level. Our result clarifies that when $α=1$ and $X$ has a symmetric Pareto distribution, the optimal rate is $n^{-1}$ rather than $n^{-1} (\ln n)^2$ as conjectured in literatures.Open AccessStable central limit theorem in total variation distance
Under certain general conditions, we prove that the stable central limit theorem holds in the total variation distance and get its optimal convergence rate for all $α\in (0,2)$. Our method is by two measure decompositions, one step estimates, and a very delicate induction with respect to $α$. One measure decomposition is light tailed and borrowed from \cite{BC16}, while the other one is heavy tailed and indispensable for lifting convergence rate for small $α$. The proof is elementary and composed of the ingredients at the postgraduate level. Our result clarifies that when $α=1$ and $X$ has a symmetric Pareto distribution, the optimal rate is $n^{-1}$ rather than $n^{-1} (\ln n)^2$ as conjectured in literatures. - 7 November 2023
- Published by American Physical Society (APS) in Physical Review E
- Vol. 108 (5) , L052104
Fluctuation theorems and thermodynamic inequalities for nonequilibrium processes stopped at stochastic times
We investigate the thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of stopping-time fluctuation theorems. We derive second-law-like thermodynamic inequalities for the mean thermodynamic functional at stochastic stopping times, the bounds of which are even stronger than the thermodynamic inequalities resulting from the traditional fluctuation theorems when the stopping time is reduced to a deterministic one. Numerical verification is carried out for three well-known thermodynamic functionals, namely, entropy production, free energy dissipation, and dissipative work. These universal equalities and inequalities are valid for arbitrary stopping strategies, and thus provide a comprehensive framework with insights into the fundamental principles governing nonequilibrium systems.
- 7 November 2023
- Published by American Physical Society (APS) in Physical Review E
- Vol. 108 (5) , L052104
Fluctuation theorems and thermodynamic inequalities for nonequilibrium processes stopped at stochastic times
We investigate the thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of stopping-time fluctuation theorems. We derive second-law-like thermodynamic inequalities for the mean thermodynamic functional at stochastic stopping times, the bounds of which are even stronger than the thermodynamic inequalities resulting from the traditional fluctuation theorems when the stopping time is reduced to a deterministic one. Numerical verification is carried out for three well-known thermodynamic functionals, namely, entropy production, free energy dissipation, and dissipative work. These universal equalities and inequalities are valid for arbitrary stopping strategies, and thus provide a comprehensive framework with insights into the fundamental principles governing nonequilibrium systems.
- Open Access
Fluctuation Theorems and Thermodynamic Inequalities for Nonequilibrium Processes Stopped at Stochastic Times
We investigate thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of stopping-time fluctuation theorems. We derive second-law-like thermodynamic inequalities for the mean thermodynamic functional at stochastic stopping times, the bounds of which are stronger than the thermodynamic inequalities resulting from the traditional fluctuation theorems when the stopping time is reduced to a deterministic one. Numerical verification is carried out for three well-known thermodynamic functionals, namely, entropy production, free energy dissipation and dissipative work. These universal equalities and inequalities are valid for arbitrary stopping strategies, and thus provide a comprehensive framework with new insights into the fundamental principles governing nonequilibrium systems.
Open AccessFluctuation Theorems and Thermodynamic Inequalities for Nonequilibrium Processes Stopped at Stochastic Times
We investigate thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of stopping-time fluctuation theorems. We derive second-law-like thermodynamic inequalities for the mean thermodynamic functional at stochastic stopping times, the bounds of which are stronger than the thermodynamic inequalities resulting from the traditional fluctuation theorems when the stopping time is reduced to a deterministic one. Numerical verification is carried out for three well-known thermodynamic functionals, namely, entropy production, free energy dissipation and dissipative work. These universal equalities and inequalities are valid for arbitrary stopping strategies, and thus provide a comprehensive framework with new insights into the fundamental principles governing nonequilibrium systems.