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1.
We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family
of representations of the infinite symmetric group. We prove that the correlation functions of the processes are given by
determinantal formulas with a certain kernel. The kernel can be expressed through the Gauss hypergeometric function; we call
it the hypergeometric kernel.
In a scaling limit our processes approximate the processes describing the decomposition of representations mentioned above
into irreducibles. As we showed in previous works, the correlation functions of these limit processes also have determinantal
form with so-called Whittaker kernel. We show that the scaling limit of the hypergeometric kernel is the Whittaker kernel.
integrable operator as defined by Its, Izergin, Korepin, and Slavnov. We argue that the hypergeometric kernel can be considered
as a kernel defining a ‘discrete integrable operator’.
We also show that the hypergeometric kernel degenerates for certain values of parameters to the Christoffel–Darboux kernel
for Meixner orthogonal polynomials. This fact is parallel to the degeneration of the Whittaker kernel to the Christoffel–Darboux
kernel for Laguerre polynomials.
Received: 22 September 1999 / Accepted: 23 November 1999 相似文献
2.
We describe the Szegő kernel on a higher genus Riemann surface in terms of Szegő kernel data coming from lower genus surfaces
via two explicit sewing procedures where either two Riemann surfaces are sewn together or a handle is sewn to a Riemann surface.
We consider in detail the examples of the Szegő kernel on a genus two Riemann surface formed by either sewing together two
punctured tori or by sewing a twice-punctured torus to itself. We also consider the modular properties of the Szegő kernel
in these cases. 相似文献
3.
简要介绍求解辐射输运方程的综合核方法,分析计算误差和收敛性,提出新的求积组和误差修正方法,提高综合核方法的计算精度.通过对基准问题的计算比对表明,采用提出的求积组并通过误差修正,综合核方法在低阶时的结果具有较高的计算精度. 相似文献
4.
G. N. Ord 《International Journal of Theoretical Physics》1993,32(2):249-260
We consider a classical Brownian motion model of diffusion in two spatial dimensions, where the Brownian particle moves on spiral paths. The classical spin does not change the propagator for the probability density for the position of the particle. However, the subdominant eigenvalues of the classical kernel are simply related to the dominant eigenvalues of the Feynman kernel for an analogous quantum system. The Feynman kernel can be extracted from the classical kernel by coupling to a spin angular momentum of the particle. 相似文献
5.
Ivan G. Avramidi 《Communications in Mathematical Physics》2009,288(3):963-1006
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation
of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole
sequence of heat invariants. We show explicitly that the obtained result correctly reproduces the first non-trivial heat kernel
coefficient as well as the exact heat kernel diagonals on the two-dimensional sphere S
2 and the hyperbolic plane H
2. We argue that the obtained formal solution correctly reproduces the exact heat kernel diagonal after a suitable regularization
and analytical continuation. 相似文献
6.
Gharakhloo Roozbeh Its Alexander R. Kozlowski Karol K. 《Letters in Mathematical Physics》2020,110(2):297-325
Letters in Mathematical Physics - We derive the large-distance asymptotics of the Fredholm determinant of the so-called generalized sine kernel at the critical point. This kernel corresponds to a... 相似文献
7.
Maria Carmela Lombardo Russel E. Caflisch Marco Sammartino 《Journal of statistical physics》2008,130(1):69-82
In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility
that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering
kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies
a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen
layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier–Stokes equations. 相似文献
8.
A. Santiago R. M. Benito 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,76(4):557-564
In this paper we present an analysis of the interplay between kernel nonlinearity and heterogeneity in preferential attachment
(PA) based network models. We define an extended class of heterogeneous PA models where the attachment kernel is a nonlinear
function of the connectivity degree of the existing network nodes. Like the original class of heterogeneous PA models, the
attachment kernel is also biased by the affinity between the states of pairs of nodes involved in a potential interaction.
We show that the class of models exhibit four kinetic regimes in their degree connectivities which are robust against the
form of heterogeneity and low-level details of the functional form of the attachment kernel. 相似文献
9.
10.
We determine running coupling corrections to the kernel of the non-linear evolution equation for the cross section of single diffractive dissociation in high energy DIS. The running coupling kernel for diffractive evolution is found to be exactly the same as the kernel of the rcBK evolution equation. 相似文献
11.
S. Caprara E. Kulatov V.V. Tugushev 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(5):1-12
We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation function is computed using a minimal phase recovering method. We illustrate our method on some examples and provide an empirical study of the estimation errors. Within this framework, we analyze high frequency financial price data modeled as 1D or 2D Hawkes processes. We find slowly decaying (power-law) kernel shapes suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics. 相似文献
12.
B. Borasoy P. C. Bruns U. -G. Meißner R. Nißler 《The European Physical Journal A - Hadrons and Nuclei》2007,34(2):161-183
We present a gauge-invariant approach to photoproduction of mesons on nucleons within a chiral unitary framework. The interaction
kernel for meson-baryon scattering is derived from the chiral effective Lagrangian and iterated in a Bethe-Salpeter equation.
Within the leading-order approximation to the interaction kernel, data on kaon photoproduction from SAPHIR, CLAS and CBELSA/TAPS
are analyzed in the threshold region. The importance of gauge invariance and the precision of various approximations in the
interaction kernel utilized in earlier works are discussed. 相似文献
13.
It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference. 相似文献
14.
We prove that the complete kernel for the high-energy evolution in QCD must be self-dual. The relevant duality transformation is formulated in precise mathematical terms and is shown to transform the charge density into the functional derivative with respect to the single-gluon scattering matrix. This transformation interchanges the high and the low density regimes. We demonstrate that the original Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner kernel, valid at large density, is indeed dual to the low density limit of the complete kernel derived recently in hep-ph/0501198. 相似文献
15.
Jonathan Breuer Yoram Last Barry Simon 《Communications in Mathematical Physics》2014,330(3):1155-1178
We study the stability of convergence of the Christoffel–Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under ? 1 and random ? 2 diagonal perturbations. We also show that convergence to the sine kernel at x implies that μ({x}) = 0. 相似文献
16.
Richard Friedberg 《Physics letters. A》2008,372(35):5734-5740
We compute the emission amplitude for the collective emission from a sphere of identical atoms in the scalar photon theory for both the cases of the complex kernel (i.e. including virtual photons) and real kernel. We explicitly show that the single mode theory based on the real kernel neglects the effects of the different decay rates and frequency shifts associated with the eigenfunctions belonging to the same angular index but with different radial indices. We show that these effects modify, for k0R?1, both the time dependence of the emission amplitude and its angular distribution, in clear contradiction to the assertions made by the Comment's authors. 相似文献
17.
F. Caporale A. Papa A. Sabio Vera 《The European Physical Journal C - Particles and Fields》2008,53(4):525-532
The use of the BFKL kernel improved by the inclusion of subleading terms generated by renormalization group (RG) analysis
has been suggested to cure the instabilities in the behavior of the BFKL Green’s function in the next-to-leading approximation
(NLA). We test the performance of a RG-improved kernel in the determination of the amplitude of a physical process, the electroproduction
of two light vector mesons, in the BFKL approach in the NLA. We find that a smooth behavior of the amplitude with the center-of-mass
energy can be achieved, setting the renormalization and energy scales appearing in the subleading terms to values much closer
to the kinematical scales of the process than in the approaches based on the unimproved kernel. 相似文献
18.
In this paper, we propose a novel classification framework using single feature kernel matrix. Different from the traditional kernel matrices which make use of the whole features of samples to build the kernel matrix, this research uses features of the same dimension of any two samples to build a sub-kernel matrix and sums up all the sub-kernel matrices to get the single feature kernel matrix. We also use single feature kernel matrix to build a new SVM classifier, and adapt SMO (Sequential Minimal Optimization) algorithm to solve the problem of SVM classifier. The results of the experiments on several artificial datasets and some challenging public cancer datasets display the classification performance of the algorithm. The comparisons between our algorithm and L2-norm SVM on the cancer datasets demonstrate that the accuracy of our algorithm is higher, and the number of support vectors selected is fewer, indicating that our proposed framework is a more practical approach. 相似文献
19.
We consider the heat kernel on the group manifold as an alternative to the Wilson action in lattice gauge theory, and we exhibit its strict analogy with the well-known Berezinski-Villain action. With the heat kernel action, the Gross-Witten singularity is rigorously absent in two dimensions. The similarity of the heat kernel action to the hamiltonian approach should provide a better convergence of the lagrangian strong coupling expansion, while its behaviour at weak coupling should simplify the analysis of the weak coupling perturbative expansion. 相似文献
20.
We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian
matrices. We show that the decomposition of a measure from this family on ergodic components is described by a determinantal
point process on the real line. The correlation kernel for this process is explicitly computed.
At certain values of parameters the kernel turns into the well-known sine kernel which describes the local correlation in
Circular and Gaussian Unitary Ensembles. Thus, the random point configuration of the sine process is interpreted as the random
set of “eigenvalues” of infinite Hermitian matrices distributed according to the corresponding measure.
Received: 22 January 2001 / Accepted: 30 May 2001 相似文献