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212
Universality for orthogonal and symplectic Laguerretype ensembles
 J. Statist. Phys
, 2007
"... Abstract. We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles of Laguerretype in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction (Theorems 1.1, 1.4, 1.6 and ..."
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Cited by 16 (0 self)
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.6 and Corollaries 1.2, 1.5, 1.7). They concern the appropriately rescaled kernels Kn,β, correlation and cluster functions, gap probabilities and the distributions of the largest and smallest eigenvalues. Corresponding results for unitary (β = 2) Laguerretype ensembles have been proved by the fourth author in [23
J.E.Adams. Robust active appearance models with iteratively rescaled kernels
 In British Machine Vision Conference
, 2007
"... Active appearance models (AAMs) are widely used to fit statistical models of shape and appearance to images, and have applications in segmentation, tracking, and classification of structures. A limitation of AAMs is that they are not robust to a large set of gross outliers. Using a robust kernel can ..."
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Cited by 3 (0 self)
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Active appearance models (AAMs) are widely used to fit statistical models of shape and appearance to images, and have applications in segmentation, tracking, and classification of structures. A limitation of AAMs is that they are not robust to a large set of gross outliers. Using a robust kernel
RESCALED LÉVYLOEWNER HULLS AND RANDOM GROWTH
, 811
"... Abstract. We consider radial Loewner evolution driven by unimodular Lévy processes. We rescale the hulls of the evolution by capacity, and prove that the weak limit of the rescaled hulls exists. We then study a random growth model obtained by driving the Loewner equation with a compound Poisson proc ..."
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Cited by 1 (0 self)
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of the limiting rescaled hulls is equal to 1. Using a different type of compound Poisson process, where the Poisson kernel is replaced by the heat kernel, as driving function, we recover one case of the aforementioned model and SLE(κ) as limits. 1. Introduction and
RESCALING WARD IDENTITIES IN THE RANDOM NORMAL MATRIX MODEL
, 2014
"... We study existence and universality of scaling limits for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward’s equation, which is an identity satisfied by the socalled Berezin kernel of the ensemble. ..."
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We study existence and universality of scaling limits for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward’s equation, which is an identity satisfied by the socalled Berezin kernel of the ensemble.
Level Spacing Distributions and the Bessel Kernel
 MATHEMATICAL PHYSICS
, 1994
"... Scaling models of random N x N hermitian matrices and passing to the limit N » oo leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others ' a ..."
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Cited by 54 (1 self)
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; as well, the kernel one obtains by scaling in the "bulk " of the spectrum is the "sine kernel" — —. Rescaling the GUE at the "edge " of the spectrum leads to the kernel π(x y) M(x)M'(y) A.. f A. f., where Ai is the Airy function. In previous
Improved Building Detection by Gaussian Processes Classification via Feature Space Rescale and Spectral Kernel Selection
"... We use spectral analysis to facilitate Gaussian processes (GP) classification. Our solution provides two improvements: scaling of the data to achieve a more isotropic nature, as well as a method to choose the kernel to match certain data characteristics. Given the dataset, from the Fourier transform ..."
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Cited by 2 (0 self)
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transform of the training data we compare the frequency domain features of each dimension to estimate a rescaling (towards making the data isotropic). Also, the spectrum of the training data is compared with several candidate kernel spectrums. From this comparison the best matching kernel is chosen
4. Proof by localization and rescaling of the DolbeaultDirac operator References
"... Abstract. We consider a general Hermitian holomorphic line bundle L on a compact complex manifold M and let qp be the Kodaira Laplacian on (0, q) forms with values in Lp. We study the scaling asymptotics of the heat kernel exp(−uqp/p)(x, y). The main result is a complete asymptotic expansion for the ..."
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Abstract. We consider a general Hermitian holomorphic line bundle L on a compact complex manifold M and let qp be the Kodaira Laplacian on (0, q) forms with values in Lp. We study the scaling asymptotics of the heat kernel exp(−uqp/p)(x, y). The main result is a complete asymptotic expansion
Scale and the differential structure of images
 Image and Vision Computing
, 1992
"... Why and how one should study a scalespace is prescribed by the universal physical law of scale invariance, expressed by the socalled Pitheorem. The fact that any image is a physical observable with an inner and outer scale bound, necessarily gives rise to a 'scalespace representation', ..."
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Cited by 116 (14 self)
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of geometrical knowledge poses additional constraints on the construction of a scalespace, notably linearity, spatial shift invariance and isotropy, thereby defining a complete hierarchical family of scaled pariial differential operators: the Gaussian kernel (the lowest order, rescaling operator) and its linear
Weak convergence of CD kernels and applications
"... Abstract. We prove a general result on equality of the weak limits of the zero counting measure, dνn, of orthogonal polynomials (defined by a measure dµ) and 1 n Kn(x, x)dµ(x). By combining this with Máté–Nevai and Totik upper bounds on nλn(x), we prove some general results on ∫ 1 I nKn(x, x)dµs → 0 ..."
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Cited by 18 (7 self)
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Abstract. We prove a general result on equality of the weak limits of the zero counting measure, dνn, of orthogonal polynomials (defined by a measure dµ) and 1 n Kn(x, x)dµ(x). By combining this with Máté–Nevai and Totik upper bounds on nλn(x), we prove some general results on ∫ 1 I nKn(x, x
Coverings, heat kernels and spanning trees
, 1999
"... We consider a graph G and a covering ˜ G of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite kregular tree and we examine the heat kernels for general kregular graphs. In particular, we show that a kregular graph on n vertices has at ..."
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Cited by 28 (9 self)
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We consider a graph G and a covering ˜ G of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite kregular tree and we examine the heat kernels for general kregular graphs. In particular, we show that a kregular graph on n vertices has
Results 1  10
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