Invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D | Zendy

Dmitry Pogosyan | Zendy; Christophe Gay | Zendy; Christophe Pichon | Zendy

Open Access

Invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D

Author(s) -

Dmitry Pogosyan,

Christophe Gay,

Christophe Pichon

Publication year - 2009

Publication title -

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Language(s) - English

Resource type - Journals

eISSN - 1550-7998

pISSN - 1550-2368

DOI - 10.1103/physrevd.80.081301

Subject(s) - mathematics , maxima and minima , hessian matrix , random field , isotropy , invariant (physics) , euler characteristic , joint probability distribution , mathematical analysis , euler's formula , computation , excursion , statistical physics , physics , mathematical physics , algorithm , statistics , quantum mechanics , political science , law

The full moments expansion of the joint probability distribution of anisotropic random field, its gradient and invariants of the Hessian is presentedin 2 and 3D. It allows for explicit expression for the Euler characteristic inND and computation of extrema counts as functions of the excursion setthreshold and the spectral parameter, as illustrated on model examples.Comment: 4 pages, 2 figures. Corrected expansion coefficients for orders n>=5. Relation between Gram-Charlier and Edgeworth expansions is clarified

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research