56 citations · 164 across the 18 of their papers we have counts for
10 papers · 1 filter
On the expected number of critical points of locally isotropic Gaussian random fields
Hao Xu, Haoran Yang, Qiang Zeng
We consider locally isotropic Gaussian random fields on the -dimensional Euclidean space for fixed . Using the so called Gaussian Orthogonally Invariant matrices first studie…
Hessian spectrum at the global minimum and topology trivialization of locally isotropic Gaussian random fields
Hao Xu, Qiang Zeng
We study the energy landscape near the ground state of a model of a single particle in a random potential with trivial topology. More precisely, we find the large dimensional limit…
Complexity of Gaussian random fields with isotropic increments: critical points with given indices
Antonio Auffinger, Qiang Zeng
We study the landscape complexity of the Hamiltonian where is a smooth Gaussian process with isotropic increments on . This mode…
Complexity of Gaussian random fields with isotropic increments
Antonio Auffinger, Qiang Zeng
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 o…
Existence of two-step replica symmetry breaking for the spherical mixed p-spin glass at zero temperature
Antonio Auffinger, Qiang Zeng
We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain c…
The SK model is infinite step replica symmetry breaking at zero temperature
Antonio Auffinger, Wei-Kuo Chen, Qiang Zeng
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 o…
Subgaussian 1-cocycles on discrete groups
Marius Junge, Qiang Zeng
We prove the Poincaré inequalities with constant for -cocycles on countable discrete groups under Bakry--Emery's -criterion. These inequalities determine…
Kolmogorov's law of the iterated logarithm for noncommutative martingales
Qiang Zeng
We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout. The key ingredient is an exponential inequality proved re…
Noncommutative martingale deviation and Poincaré type inequalities with applications
Marius Junge, Qiang Zeng
We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with sati…
Noncommutative Bennett and Rosenthal inequalities
Marius Junge, Qiang Zeng
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal i…