Related papers: Logarithm laws and shrinking target properties
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…
The two-dimensional shallow water equations in Eulerian and Lagrangain coordinates are considered. Lagrangian and Hamiltonian formalism of the equations is given. The transformations mapping the two-dimensional shallow water equations with…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results…
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the…
Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear…
We give upper and lower bounds for Diophantine exponents measuring how well a point in the plane can be approximated by points in the orbit of a lattice $\Gamma<\mathrm{SL}_2(\mathbb{R})$ acting linearly on $\mathbb{R}^2$. Our method gives…
We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.
Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the…
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like…
Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…
A systematic approach to finding variational approximation in an otherwise intractable non-conjugate model is to exploit the general principle of convex duality by minorizing the marginal likelihood that renders the problem tractable. While…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…