相关论文: Inside singularity sets of random Gibbs measures
We study a problem with three equivalent formulations: describing Gibbs measures for five-vertex model in quadrant; classifying coherent systems on a p-deformation of the Gelfand-Tsetlin graph related to Grothendieck polynomials; finding…
In this paper, we show that Gibbs measures on self-conformal sets generated by a $C^{1+\alpha}$ conformal IFS on $\mathbb{R}^d$ satisfying the OSC are exponentially mixing. We exploit this to obtain essentially sharp asymptotic counting…
We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the…
In this paper, we explore the conformal structure of singularities arising from varying fundamental constants using the method of Penrose diagrams. We employ a specific type of bimetric model featuring two different metrics. One metric…
We show that if a discrete random measure on the unit ball of a separable Hilbert space satisfies the Ghirlanda-Guerra identities then by randomly deleting half of the points and renormalizing the weights of the remaining points we obtain…
On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical…
We introduce a segmentation algorithm to probe temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local values of heart rates follow a power-law…
We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…
Multifractal analysis is a powerful approach for characterizing ergodic or localized nature of eigenstates in complex quantum systems. In this context, the eigenvectors of random matrices belonging to invariant ensembles naturally serve as…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range.…
A class of spectral subgrid models based on a self-similar and reversible closure is studied with the aim to minimize the impact of subgrid scales on the inertial range of fully developed turbulence. In this manner, we improve the scale…
We study the growth rate of a sequence which measures the uniform norm of the differential under the iterates of maps. On symplectically hyperbolic manifolds, we show that this sequence has at least linear growth for every non-identical…
While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not…
In this article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. The classical construction of the SRB measure is based on…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…
In a recent article, we showed that trigonometric shearlets are able to detect directional step discontinuities along edges of periodic characteristic functions. In this paper, we extend these results to multivariate periodic functions…