14 papers
Dimension-free Riesz transform estimates on biased hypercubes via non-tracial baby Fock models
Hun Hee Lee, Zhendong Xu, Sang-gyun Youn +1
We study dimension-free Riesz transform estimates on hypercubes equipped with non-uniform product measures. For , we prove a dimension-free Meyer inequality for the…
The Endpoint Fractional Riesz Estimate on the Hamming Cube
Zhendong Xu, Hao Zhang
Let and be the discrete partial derivative on the Hamming cube . Let be the discrete Laplacian. We prove the endpoint inequali…
Hypercontractivity for a family of quantum Ornstein-Uhlenbeck semigroups
Longfa Sun, Zhendong Xu, Hao Zhang
We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant. The main ingredient of ou…
Average first-passage times for character sums
Quanyu Tang, Hao Zhang
Let and, for an odd prime , set Define the first-passage time $$ f_\varepsilon(p):=\min\{\ell\ge 1:\ S…
Theory of Remaining Exceptional Points from Nongeneric Splitting in Non-Hermitian Systems
Teng Yin, Hao Zhang
In non-Hermitian physics, high-order exceptional points(HOEPs) with eigenvalues and eigenvectors coalesce are known for their enhanced sensitivity to perturbations. Typically, they…
Towards Quantum Simulations of Sphaleron Dynamics at Colliders
Min Huang, Ying-Ying Li, Yandong Liu +1
Sphaleron dynamics in the Standard Model at high-energy particle collisions remains experimentally unobserved, with theoretical predictions hindered by its nonperturbative real-tim…
Quantum Properties of Non-Dirichlet Boundary Conditions in Gravity
Patrick Draper, Manthos Karydas, Hao Zhang
The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Diric…
Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions
Motoo Suzuki, Ling-Xiao Xu, Hao Y. Zhang
We generalize the framework of spurion analysis to a class of selection rules arising from non-invertible fusion algebras in perturbation theory. As a first step toward systematic…
Complex median method and Schatten class membership of commutators
Zhenguo Wei, Hao Zhang
This article is devoted to the study of the Schatten class membership of commutators involving singular integral operators. We utilize martingale paraproducts and Hytönen's dyadic…
Weighted norm inequalities of various square functions and Volterra integral operators on the unit ball
Changbao Pang, Maofa Wang, Bang Xu +1
In this paper, we investigate various square functions on the complex unit ball. We prove the weighted inequalities of the Lusin area integral associated with Poisson integral in t…
On the boundedness and Schatten class property of noncommutative martingale paraproducts and operator-valued commutators
Zhenguo Wei, Hao Zhang
We study the Schatten class membership of semicommutative martingale paraproducts and use the transference method to describe Schatten class membership of purely noncommutative mar…
Best constants in the vector-valued Littlewood-Paley-Stein theory
Guixiang Hong, Zhendong Xu, Hao Zhang
Let be a sectorial operator of type () on with the kernels of satisfying certain size and regularity conditions. Defi…
On the best constants of the noncommutative Littlewood-Paley-Stein inequalities
Zhenguo Wei, Hao Zhang
Let . Let be a noncommutative symmetric diffusion semigroup on a semifinite von Neumann algebra , and let be its associated…
Boundedness of operator-valued commutators involving martingale paraproducts
Zhenguo Wei, Hao Zhang
Let . We show the boundedness of operator-valued commutators on the noncommutative for any von Neumann algebr…