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Chunsheng Ma

Publications and source records attributed to Chunsheng Ma.

7 recordsLinked to original sources
arXiv2021

Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces

This paper is concerned with sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the high-frequency behavior of its angular power spectrum, and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.

math.PR↗
arXiv2020

Evidence of the Berezinskii-Kosterlitz-Thouless Phase in a Frustrated Magnet

The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. Here, we pin down two transitions that bound a BKT phase in an ideal 2D frustrated magnet TmMgGaO$_4$, via nuclear magnetic resonance under in-plane magnetic fields, which do not disturb the low-energy electronic states and allow BKT fluctuations to be detected sensitively. Moreover, by applying out-of-plane fields, we find a critical scaling behaviour of the magnetic susceptibility expected for the BKT transition. The experimental findings can be explained by quantum Monte Carlo simulations applied on an accurate triangular-lattice Ising model of the compound which hosts a BKT phase. These results provide a concrete example for the BKT phase and offer an ideal platform for future investigations on the BKT physics in magnetic materials.

cond-mat.str-el↗
arXiv2019

Isotropic covariance matrix functions on compact two-point homogeneous spaces

The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and sufficient conditions are derived for a symmetric and continuous matrix function to be an isotropic covariance matrix function on all compact two-point homogeneous spaces. It is also shown that, for a symmetric and continuous matrix function with compact support, if it makes an isotropic covariance matrix function in the Euclidean space, then it makes an isotropic covariance matrix function on the sphere or the real projective space.

math.PR↗
arXiv2018

Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field, which involve Jacobi polynomials and the distance defined on the compact two-point homogeneous space.

math.PR↗
arXiv2016

Time varying axially symmetric vector random fields on the sphere

This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The series representation is somehow an imitator of the covariance matrix function, and both of them have simpler forms than those proposed in the literature in terms of the associated Legendre functions and are useful for modeling and simulation. Also, a general form of the covariance matrix structure is derived for a spatio-temporal vector random field that is axially symmetric and mean square continuous over the sphere, and a series representation is given for a longitudinally reversible one.

math.PR↗
arXiv2016

Time Varying Isotropic Vector Random Fields on Spheres

For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random field, which involve the ultraspherical polynomials. The series representation is somehow an imitator of the covariance matrix function, but differs from the the spectral representation in terms of the ordinary spherical harmonics, and is useful for modeling and simulation. Some semiparametric models are also illustrated.

math.PR↗