Consistent estimates of deformed isotropic Gaussian random fields on the plane, Ann. Statist, vol.37, issue.5A, pp.2324-2350, 2009. ,
The Geometry of Random Fields, 1981. ,
A generalized quadratic estimate for random field nonstationarity, 2016. ,
Level crossings for random fields, Ann. Probab, vol.4, pp.1-12, 1976. ,
DOI : 10.1214/aop/1176996176
URL : https://doi.org/10.1214/aop/1176996176
Geometrical characteristics of Gaussian sea waves, Journal of Applied Probability, vol.42, issue.2, pp.407-425, 2005. ,
Rice formulae and Gaussian waves, Bernoulli, vol.17, pp.170-193, 2011. ,
Palm distributions of wave characteristics in encountering seas, The Annals of Applied Probability, vol.18, issue.3, pp.1059-1084, 2008. ,
Estimating deformations of isotropic Gaussian random fields on the plane, Ann. Statist, vol.36, issue.2, pp.719-741, 2008. ,
Anisotropy models for spatial data, Mathematical Geosciences, vol.48, issue.3, pp.305-328, 2016. ,
DOI : 10.1007/s11004-015-9594-x
URL : https://hal.archives-ouvertes.fr/hal-01183245
Random Fields and Geometry, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-01975050
On the distribution of the maximum of a Gaussian field with d parameters, Ann. Appl. Probab, vol.15, pp.254-278, 2005. ,
Level sets and extrema of random processes and fields, 2009. ,
Two point function for critical points of a random plane wave, 2017. ,
Phase singularities in isotropic random waves, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.456, pp.2059-2079, 2000. ,
DOI : 10.1098/rspa.2000.0602
Anisotropic analysis of some Gaussian models, Journal of Fourier Analysis and Applications, vol.9, issue.3, pp.215-236, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00087790
On the number of crossings of a level by a Gaussian random process. i, Theory of Probability & Its Applications, vol.11, pp.106-113, 1966. ,
Regular and irregular semiclassical wavefunctions, Journal of Physics A: Mathematical and General, vol.10, issue.12, p.2083, 1977. ,
DOI : 10.1142/9789813221215_0023
Estimation of local Anisotropy based on level sets, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01676491
Isotropic diffeomorphisms: solutions to a differential system for a deformed random fields study, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01496514
Kac-Rice formulas for random fields and their applications in random geometry, roots of random polynomials and some engineering problems, Ediciones IVIC, Instituto Venezolano de Investigaciones Científicas, 2017. ,
A turning-band method for the simulation of anisotropic fractional Brownian fields, Journal of Computational and Graphical Statistics, vol.24, issue.3, 2015. ,
Monotone Funktionen, Stieltjessche Integrale und harmonische Analyse, Math. Ann, vol.108, pp.378-410, 1933. ,
DOI : 10.1007/bf01452844
On the mean number of crossings of a level by a stationary Gaussian process, Theory Probab. Appl, vol.6, pp.435-438, 1961. ,
Affine processes: A test of isotropy based on level sets, SIAM Journal on Applied Mathematics, vol.47, issue.4, pp.886-891, 1987. ,
Stationary and Related Stochastic Processes, 1967. ,
The texture gradient equation for recovering shape from texture, IEEE Trans. Pattern Anal. Mach. Intell, vol.24, issue.4, pp.536-549, 2002. ,
Estimating deformations of stationary processes, The Annals of Statistics, vol.31, issue.6, pp.1772-1821, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00150387
Conditions for finite moments of the number of zero crossings for Gaussian processes, Ann. Probab, vol.3, issue.5, pp.849-858, 1975. ,
A test of Gaussianity based on the Euler characteristic of excursion sets, Electronic Journal of Statistics, vol.11, issue.1, pp.843-890, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01345225
Number of critical points of a Gaussian random field: condition for a finite variance, Statistics & Probability Letters, vol.118, pp.94-99, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01374125
Anisotropic random wave models, 2018. ,
A central limit theorem for the Euler characteristic of a Gaussian excursion set, Annals of Probability, vol.44, issue.6, pp.3849-3878, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00943054
On the variance of the number of stationary points of a homogeneous Gaussian field, Theory of Probability & Its Applications, vol.29, pp.569-570, 1985. ,
Estimation of space deformation model for non-stationary random functions, Spatial Statistics, vol.13, pp.45-61, 2015. ,
DOI : 10.1016/j.spasta.2015.05.001
URL : https://hal.archives-ouvertes.fr/hal-01090350
Identification and isotropy characterization of deformed random fields through excursion sets, 2018. ,
DOI : 10.1017/apr.2018.32
URL : https://hal.archives-ouvertes.fr/hal-01495157
On the variance of the number of zeros of a stationary Gaussian process, Ann. Math. Statist, vol.43, issue.3, pp.977-982, 1972. ,
Identification of space deformation using linear and superficial quadratic variations, Statistics & Probability Letters, vol.47, issue.3, pp.307-316, 2000. ,
DOI : 10.1016/s0167-7152(99)00171-6
URL : https://hal.archives-ouvertes.fr/hal-00273111
Mass reconstruction with cosmic microwave background polarization, The Astrophysical Journal, vol.574, issue.2, pp.566-574, 2002. ,
DOI : 10.1086/341110
URL : http://iopscience.iop.org/article/10.1086/341110/pdf
On the average number of real roots of a random algebraic equation, Bull. Am. Math. Soc, vol.27, issue.1, pp.83-96, 1943. ,
Nodal length fluctuations for arithmetic random waves, Annals of Mathematics, vol.177, issue.2, pp.699-737, 2013. ,
DOI : 10.4007/annals.2013.177.2.8
URL : http://annals.math.princeton.edu/wp-content/uploads/annals-v177-n2-p08-p.pdf
On the second moment of the number of crossings by a stationary Gaussian process, Annals of Probability, vol.34, issue.4, pp.1601-1607, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00179359
Morphometry of random spatial structures in physics, 2016. ,
On probability measures arising from lattice points on circles, Mathematische Annalen, vol.367, issue.3, pp.1057-1098, 2017. ,
DOI : 10.1007/s00208-016-1411-4
URL : https://link.springer.com/content/pdf/10.1007%2Fs00208-016-1411-4.pdf
Introduction to Topological Manifolds, 2000. ,
The statistical analysis of a random, moving surface, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol.249, issue.966, pp.321-387, 1957. ,
Slepian models for the stochastic shape of individual Lagrange sea waves, Advances in Applied Probability, vol.38, issue.2, pp.430-450, 2006. ,
, Modern Directional Statistics, 2017.
DOI : 10.1201/9781315119472
On conditions for finiteness of the factorial moments of the number of zeros of Gaussian stationary processes, Theory of Probability & Its Applications, vol.29, pp.534-545, 1985. ,
Critical Point Theory in Global Analysis and Differential Topology: An Introduction, 1969. ,
, Directional Statistics, 2009.
Non-universality of nodal length distribution for arithmetic random waves. Geometric and Functional Analysis, vol.26, pp.926-960, 2016. ,
DOI : 10.1007/s00039-016-0376-5
URL : http://arxiv.org/pdf/1508.00353
, Nodal statistics of planar random waves, 2017.
DOI : 10.1007/s00220-019-03432-5
URL : http://arxiv.org/pdf/1708.02281
Detecting directionality in random fields using the monogenic signal, Planck 2015 results -XVI. Isotropy and statistics of the CMB, vol.60, pp.6491-6510, 2014. ,
DOI : 10.1109/tit.2014.2342734
URL : http://arxiv.org/pdf/1304.2998.pdf
Wavelet-based orientation of localizable Gaussian fields, 2017. ,
Identifiability for non-stationary spatial structure, Journal of Applied Probability, vol.36, issue.4, pp.1244-1250, 1999. ,
DOI : 10.1017/s0021900200018027
Reducing non-stationary random fields to stationarity and isotropy using a space deformation, Statistics & Probability Letters, vol.48, issue.1, pp.23-32, 2000. ,
DOI : 10.1016/s0167-7152(99)00188-1
Statistical tests of anisotropy for fractional Brownian textures. application to full-field digital mammography, Journal of Mathematical Imaging and Vision, vol.36, issue.3, pp.227-240, 2010. ,
DOI : 10.1007/s10851-009-0181-y
URL : https://hal.archives-ouvertes.fr/hal-00177770
Mathematical analysis of random noise, Bell Syst. Tech. J, vol.23, pp.282-332, 1944. ,
DOI : 10.1002/j.1538-7305.1944.tb00874.x
URL : http://dml.cz/bitstream/handle/10338.dmlcz/103399/AplMat_17-1972-2_1.pdf
On the volume of nodal sets for eigenfunctions of the Laplacian on the torus, Annales Henri Poincaré, vol.9, issue.1, pp.109-130, 2008. ,
Nonparametric estimation of nonstationary spatial covariance structure, Journal of the American Statistical Association, vol.87, issue.417, pp.108-119, 1992. ,
DOI : 10.2307/2290458
Simulation of multivariate and multidimensional random processes, The Journal of the Acoustical Society of America, vol.49, issue.1B, pp.357-368, 1971. ,
Digital simulation of random processes and its applications, Journal of Sound Vibration, vol.25, pp.111-128, 1972. ,
A note on the higher moments of the Euler characteristic of the excursion sets of random fields, Statistics & Probability Letters, vol.79, issue.8, pp.1074-1082, 2009. ,
Validity of the expected Euler characteristic heuristic, Ann. Prob, vol.33, issue.4, pp.357-368, 2005. ,