相关论文: Markov spectra for modular billiards

In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the…

For piecewise monotone interval maps we look at Birkhoff spectra for regular potential functions. This means considering the Hausdorff dimension of the set of points for which the Birkhoff average of the potential takes a fixed value. In…

We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.

We consider periodic Jacobi operators and obtain upper and lower estimates on the sizes of the spectral bands. Our proofs are based on estimates on the logarithmic capacities and connections between the Chebyshev polynomials and logarithmic…

For the almost Mathieu operator with a small coupling constant, for a series of spectral gaps, we describe the asymptotic locations of the gaps and get lower bounds for their lengths. The results are obtained by analysing a monodromy…

The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…

The lower spectral radius, or joint spectral subradius, of a set of real $d \times d$ matrices is defined to be the smallest possible exponential growth rate of long products of matrices drawn from that set. The lower spectral radius arises…

We clarify from a general perspective, the condition for the appearance of chaotic energy spectrum in quantum pseudointegrable billiards with a point scatterer inside.

This short piece defines a Markov basis. The aim is to introduce the statistical concept to mathematicians.

We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…

With the help of the representation of SL(2,Z) on the rank two free module over the integer adeles, we define the transition operator of a Markov chain. The real component of its spectrum exhibits a gap, whereas the non-real component forms…

We study the quantal energy spectrum of triangular billiards on a spherical surface. Group theory yields analytical results for tiling billiards while the generic case is treated numerically. We find that the statistical properties of the…

We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the…

In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and non-integrable…

We give some remarks on limit mixed Hodge structure and spectrum. These are more or less well-known to the specialists, and do not seem to be stated explicitly in the literature. However, they do not seem to be completely trivial to the…

Polygonalization of any smooth billiard boundary can be carried out in several ways. We show here that the semiclassical description depends on the polygonalization process and the results can be inequivalent. We also establish that…

The representation problem of finite-dimensional Markov matrices in Markov semigroups is revisited, with emphasis on concrete criteria for matrix subclasses of theoretical or practical relevance, such as equal-input, circulant, symmetric or…

We analyze "Neumann" spectral minimal partitions for a thin strip on a cylinder or for the thin annulus.

We present numerical results on calculations of energy spectra and wave functions of annular billiard.

In this work we present the results of a study of spectral statistics for a classically integrable system, namely the rectangle billiard. We show that the spectral statistics are indeed Poissonian in the semiclassical limit for almost all…