相关论文: Multiscale Analysis and Localization of Random Ope…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability…
This paper presents optimizations to improve the scalability of reachability analysis on a subclass of hybrid automata extended with stochasticity. The optimizations target different components of the analysis, such as quantifier…
Study of fine spectral properties of quasiperiodic and similar discrete Schr\"odinger operators involves dealing with problems caused by small denominators, and until recently was only possible using perturbative methods, requiring certain…
The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schr\"odinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures…
We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…
We prove a Wegner estimate for a large class of multiparticle Anderson Hamiltonians on the lattice. These estimates will allow us to prove Anderson localization for such systems. A detailed proof of localization will be given in a…
The problem of multi-speaker localization is formulated as a multi-class multi-label classification problem, which is solved using a convolutional neural network (CNN) based source localization method. Utilizing the common assumption of…
In a previous paper (Varadi et al., 1999), Random Lag Singular Spectrum Analysis was offered as a tool to find oscillations in very noisy and long time series. This work presents a generalization of the technique to search for common…
We consider Schr\"odinger operators on $L^2(R^d)$ with a random potential concentrated near the surface $R^{d_1}\times\{0\}\subset R^d $. We prove that the integrated density of states of such operators exhibits Lifshits tails near the…
In this paper, we use Cartan estimate for meromorphic functions to prove Anderson localization for a class of long-range operators with singular potenials.
Anderson localization provides a challenge to numerical approaches due to the inherent randomness, and hence absence of simple symmetries, in its discrete Hamiltonian representation. Numerous algorithmic approaches have been developed or…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
This work relates quantitatively homogenization to Anderson localization for acoustic operators in disordered media. By blending dispersive estimates for homogenized operators and quantitative homogenization of the wave equation, we derive…
This paper contains a study of multivariate second order stochastic mappings indexed by an abstract set $\Lambda$ in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert…
This is the material for two lectures given at Ecole Polytechnique in May 2011 for the math teachers of "classes pr\'eparatoires"(parallel to the undergraduate classes in universities). The introduction is a personal overview on Fourier…
We discuss generalizations of Rubio de Francia's inequality for Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two versions of Rubio de Francia's operator are discussed: it is shown that a rotation factor is needed…
The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the…
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…