Related papers: Free divisors versus stability and coincidence thr…
Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $\Sigma$ with an additional assumption that $\Sigma$ can be represented as a sum of a few Kronecker products…
We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the…
We establish a general theory for projective dimensions of the logarithmic derivation modules of hyperplane arrangements. That includes the addition-deletion and restriction theorem, Yoshinaga-type result, and the division theorem for…
We give the first example of systolic freedom over torsion coefficients. The phenomenon is a bit unexpected (contrary to a conjecture of Gromov's) and more delicate than systolic freedom over the integers.
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the case where the deviation is measured in terms of the…
We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
In the study of classical obstacle problems, it is well known that in many configurations the free boundary intersects the fixed boundary tangentially. The arguments involved in producing results of this type rely on the linear structure of…
We address the flutter instability of a flexible plate immersed in an axial flow. This instability is similar to flag flutter and results from the competition between destabilising pressure forces and stabilising bending stiffness. In…
It has been known for years how random height variations of a repeated nano-scale structure can give rise to smooth angular color variations instead of the well-known diffraction pattern experienced if no randomization is present. However,…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
We study the question of when a (\{0,1\})-valued threshold process associated to a mean zero Gaussian or a symmetric stable vector corresponds to a {\it divide and color (DC) process}. This means that the process corresponding to fixing a…
We study the relation between perverse stability conditions and geometric stability conditions under blow up. We confirm a conjecture of Toda in some special cases and show that geometric stability conditions can be induced from perverse…
We establish a near dichotomy between randomness and structure for the point counts of arbitrary projective cubic threefolds over finite fields. Certain "special" subvarieties, not unlike those in the Manin conjectures, dominate. We also…
We investigate the crossover between weak and strong self-avoidance in a simulation of random surfaces with extrinsic curvature. We consider both dynamically triangulated and rigid surfaces with the two possible discretizations of the…
This paper derives sufficient conditions for superconvergence of sums of bounded free random variables and provides an estimate for the rate of superconvergence.
Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case…
We present three measures of the dynamical coherence of channels, which are the generalization of several previous results. The measures are based on the generalized distance function between channels, which for example could be the…
This article is concerned with the dynamic behaviour of two immiscible and incompressible fluids in a cylindrical domain, which are separated by a sharp interface. In case that the heavy fluid is situated on top of the light fluid, one…