Dr. Deping Ye

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Research Interests

Convex geometry, geometric analysis, and geometric functional analysis

Functional inequalities and geometric inequalities

Quantum information theory

Random matrices and compressed sensing

Statistical models with measurement error

Research Grants

2018-2023, A 5-year NSERC grant

2012-2018, A 6-year NSERC grant (with a supplement for early career researchers)

2011-2013, A startup grant from Memorial University of Newfoundland

Publications

Convex Geometry

R. Gardner, D. Hug, S. Xing and D. Ye, General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem II. Submitted. arXiv:1809.09753

R. Gardner, D. Hug, W. Weil, S. Xing and D. Ye, General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem I. Calc. Var. PDE., in press.

S. Xing and D. Ye, On the general dual Orlicz-Minkowski problem. Indiana Univ. Math. J., in press.

B. Zhu, S. Xing and D. Ye, The dual Orlicz-Minkowski problem. J. Geom. Anal., in press.

B. Zhu, H. Hong and D. Ye, The Orlicz-Petty bodies. Int. Math. Res. Notices, 2018 (2018) 4356-4403.

D. Ye, Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\phi}$ affine and geominimal surface areas. J. Math. Anal. Appl., 443 (2016) 352-371.

D. Ye, B. Zhu and J. Zhou, The mixed $L_p$ geominimal surface areas for multiple convex bodies. Indiana Univ. Math. J., 64 (2015) 1513-1552.

R.J. Gardner, D. Hug, W. Weil and D. Ye, The Dual Orlicz-Brunn-Minkowski Theory. J. Math. Anal. Appl., 430 (2015) 810-829.

Note: the article arXiv:1404.6991 (by myself) will not be submitted for publication.

D. Ye, $L_p$ Geominimal Surface Areas and their Inequalities. Int. Math. Res. Notes, 2015 (2015) 2465-2498.

D. Ye, New Orlicz Affine Isoperimetric Inequalities. J. Math. Anal. Appl., 427 (2015) 905-929.

D. Ye, On the monotone properties of general affine surface areas under the Steiner symmetrization. Indiana Univ. Math. J., 63 (1) (2014) 1-19.

D. Ye, Inequalities for general mixed affine surface areas. J. London Math. Soc., 85 (2012) 101-120.

E. Werner and D. Ye, On the Homothety Conjecture. Indiana Univ. Math. J., 60 (2011) 1-20.

E. Werner and D. Ye, Inequalities for mixed $p$-affine surface area. Math. Ann., 347 (3) (2010) 703-737.

E. Werner and D. Ye, New $L_p$ Affine Isoperimetric Inequalities. Adv. Math., 218 (2008) 762-780.

Capacity

X. Luo, D. Ye and B. Zhu, On the polar Orlicz-Minkowski problems and the $p$-capacitary Orlicz-Petty bodies. Indiana Univ. Math. J., in press.

H. Hong and D. Ye, Sharp geometric inequalities for the general $p$-affine capacity. J. Geom. Anal., 28 (2018) 2254-2287.

H. Hong, D. Ye and N. Zhang, The $p$-capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems. Calc. Var. PDE., 57:5 (2018) 1-31.

S. Hou, J. Xiao and D. Ye, A mixed volume from the anisotropic Riesz-potential. Trans. London Math. Soc., 5 (2018) 71-96.

J. Xiao and D. Ye, Anisotropic Sobolev Capacity with Fractional Order. Canad. J. Math., 69 (2017) 873-889.

Functional Inequalities and Theory of $f$-divergence

S. Hou and D. Ye, Orlicz addition for measures and an optimization problem for the $f$-divergence. Submitted.

E. Werner and D. Ye, Mixed $f$-divergence for multiple pairs of measures. Canad. Math. Bull., 60 (2017) 641-654.

U. Caglar and D. Ye, Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory. Adv. Appl. Math., 81 (2016) 78-114.

Quantum Information Theory

G. Aubrun, S. Szarek and D. Ye, Entanglement thresholds for random induced states. Comm. Pure Appl. Math., 67 (1) (2014) 129-171.

B. Collins, I. Nechita and D. Ye, The absolute positive partial transpose property for random induced states. Random Matrices Theory Appl., 1 (2012) 1250002 (22 pages).

G. Aubrun, S. Szarek and D. Ye, Phase transitions for random states and a semi-circle law for the partial transpose. Phys. Rev. A, 85 (2012) 030302(R), 4 pages.

D. Ye, On the comparison of volumes of quantum states. J. Phys. A, 43 (2010) 315301 (17pp).

D. Ye, On the Bures volume of separable quantum states. J. Math. Phys., 50 (2009) 083502.

Nonparametric Estimation

X.F. Wang and D. Ye, Conditional density estimation in measurement error problems. J. Multivariate Anal., 133 (2015) 38-50.

X.F. Wang and D. Ye, The effects of error magnitude and bandwidth selection for deconvolution with unknown error distribution. J. Nonparametr. Stat., 24 (2012) 153-167.

X.F. Wang, B. Wang and D. Ye, Computational aspects in local image denoising and reconstruction with correlated errors. Amer. J. Math. Management Sci., 30 (2010) 197-215.

X.F. Wang and D. Ye, On nonparametric comparison of images and regression surfaces. J. Statist. Plann. Inference, 140 (2010) 2875-2884.