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The article is devoted to the geometry of solutions to the chordal Loewner equation which is based on comparison of singular solutions and harmonic measures for the sides of a slit in domains generated by a driving term. It is proved that…
In this paper we consider a family of three-dimensional problems in thermoelasticity for linear elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero.We fully characterize with strong…
We study random spherical harmonics at shrinking scales. We compare the mass assigned to a small spherical cap with its area, and find the smallest possible scale at which, with high probability, the discrepancy between them is small…
The effective dynamics of solitons for the generalized nonlinear Schr\"odinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton,…
The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivations arising from Physics and Cosmology. In this paper, we are concerned…
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface…
A lot of efforts have been devoted in the last decade to the investigation of the high-frequency behaviour of geometric functionals for the excursion sets of random spherical harmonics, i.e., Gaussian eigenfunctions for the spherical…
In these notes, we describe the recent progress in understanding the zero sets of two remarkable Gaussian random functions: the Gaussian entire function with invariant distribution of zeroes with respect to isometries of the complex plane,…
In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties…
We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic domain, i.e., it allows the corresponding support in multipole (frequency) space to vary in more general forms than…
In this paper, we will revisit the Slepian spatiospectral concentration problem for the spherical Fourier-Bessel band-limited spaces introduced for 3-D domain, and discuss its general form in $\mathbb{R}^d$, $d\geq 2$. In particular, we…
We study the asymptotic behaviour of both spherical $t$-designs and random uniform designs as the set of sampling points in non-parametric regression with spherical regressors of arbitrary dimension. We show that the corresponding…
We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of…
The $N=2$ fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact $N=4$ fermionic string model. The issues of space-time Lorentz covariance and supersymmetry for the BRST quantized $N=2$ strings…
The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's…
We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the interior nodal sets is obtained for Robin eigenfunctions in the smooth domain.…
We investigate Stein-Malliavin approximations for nonlinear functionals of geometric interest of Gaussian random eigenfunctions on the unit $d$ -dimensional sphere ${\mathbb{S}}^{d},$ $d\geq 2.$ All our results are established in the high…