Related papers: Measures and Jacobians of singular random matrices
We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these…
We study the singularity of Quillen metrics for one-parameter degenerations of compact Kaehler manifolds.
Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian motion. A necessary and sufficient explicit condition…
The article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields such as: convolutions of measures and functions; continuity of functions of measures; non-associative noncommutative…
In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable…
The topic of this paper concerns a certain relation between the jacobians of various quotients of the modular curve $X(p)$, which relates the jacobian of the quotient of $X(p)$ by the normaliser of a non-split Cartan subgroup of $GL_2(F_p)$…
In this paper, the moment problem for symmetric probability measures is characterized in terms of associated sequences called Jacobi sequences $\{\omega_n\}$. A notion named property (SC), which is proved to be a necessary and sufficient…
This work presents results on the finiteness, and on the symmetry properties, of various homological dimensions associated to the Jacobson radical and its higher syzygies, of a semiperfect ring.
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward…
We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated to groups of maps on affine spaces.
We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [17] for spectral measures of classical ensembles (Gauss-Hermite, Laguerre,…
We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several…
We find explicit equations for two-coverings of Jacobians of genus two curves over an arbitrary ground field of characteristic different from two.
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
The Hamiltonian formulation for a non-Abelian gauge theory in two spatial dimensions is carried out in terms of a gauge-invariant matrix parametrization of the fields. The Jacobian for the relevant transformation of variables is given in…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
The Polyakov measure for the Abelian gauge field is considered in the Robertson-Walker spacetimes. The measure is concretely represented by adopting two kind of decompositions of the gauge field degrees of freedom which are most familiarly…
We study finite dimensional semisimple Hopf algebra actions on noetherian connected graded Artin-Schelter regular algebras, and introduce definitions of the Jacobian, the reflection arrangement and the discriminant in a noncommutative…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
In this survey we discuss some of the classical and modern methods in studying the (Riemann-)Schottky problem, the problem of characterizing Jacobians of curves among principally polarized abelian varieties. We present many of the recent…