相关论文: Inside singularity sets of random Gibbs measures

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.

We define a large class of multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal…

We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…

Lagrangian acceleration has been investigated both experimentally and numerically in the past, and it has been shown to exhibit extreme fluctuations, which have been rationalized as events in which tracer particles get trapped into vortical…

We consider multiple and set-indexed sums of random vectors taking values in Euclidean space of growing dimension. It is shown that, when viewed as finite metric spaces, the sets of values of such sums converge in probability. The limit is…

We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…

Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…

In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of…

The failure probabilities or the strength distributions of heterogeneous 1D systems with continuous local strength distribution and local load sharing have been studied using a simple, exact, recursive method. The fracture behavior depends…

We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…

We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this…

Aims. We analyze and characterize the angular distribution of selected samples of gamma ray bursts (GRBs) from Batse and Swift data to confirm that the division in two classes of short- and long-duration GRBs correspond also to the…

The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase…

Detecting and analyzing directional structures in images is important in many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. Classifying a structure as directional…

In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in the Hilbert space, support of the eigenstates. In this work, using exact…

We study the Gibbs measure of the nonhierarchical versions of the Generalized Random Energy Models introduced in previous work. We prove that the ultrametricity holds only provided some nondegeneracy conditions on the hamiltonian are met.

We study the scaling scenery of Gibbs measures for subshifts of finite type on self-conformal fractals and applications to Falconer's distance set problem and dimensions of projections. Our analysis includes hyperbolic Julia sets, limit…

Multiplicative cascades have been used in turbulence to generate fields with multifractal statistics and long-range correlations. Examples of continuous and causal stochastic processes which generate such a random field have been carefully…

Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific…

This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base…