Related papers: Asymptotic Pairs for Interval Exchange Transformat…

We show that minimal shifts with zero topological entropy are topologically conjugate to interval exchange transformations, generally infinite. When these shifts have linear factor complexity (linear block growth), the conjugate interval…

We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (cf…

We establish an asymptotic formula for the number of integral solutions of bounded height for pairs of diagonal quartic equations in $26$ or more variables. In certain cases, pairs in $25$ variables can be handled.

Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…

We study statistical properties of the random variables $X_{\sigma}(\pi)$, the number of occurrences of the pattern $\sigma$ in the permutation $\pi$. We present two contrasting approaches to this problem: traditional probability theory and…

We show that the typical measure preserving transformation is not isomorphic to any interval exchange transformation.

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…

It is shown that in asymptotic transition from Fourier series to integrals an error and ambiguity may arise. Ambiguity reduces to a possibility of addition of some distribution to the result. Properties of such distributions are studied and…

The asymptotic normality in multi-dimension of the nonparametric estimator of the transition probabilities of a Markov renewal chain is proved, and is applied to that of other nonparametric estimators involved with the associated…

We study higher-order asymptotic expansions of eigenvalues in perturbed transfer operators, of the corresponding eigenfunctions and of the corresponding eigenvectors of the dual operators. In our main result, we give explicit expressions of…

We compute the asymptotic probability that a random pair of Sylow 2-subgroups in $S_n$ or $A_n$ intersects trivially. This calculation complements recent work of Diaconis, Giannelli, Guralnick, Law, Navarro, Sambale, and Spink (see…

We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…

The spatial sign correlation (D\"urre, Vogel and Fried, 2015) is a highly robust and easy-to-compute, bivariate correlation estimator based on the spatial sign covariance matrix. Since the estimator is inefficient when the marginal scales…

Dynamically varying system parameters along a path enclosing an exceptional point is known to lead to chiral mode conversion. But is it necessary to include this non-Hermitian degeneracy inside the contour for this process to take place? We…

In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the…

We consider general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. We present asymptotic formulas for change of slow variables at evolution across…

For non-singular intersections of pairs of quadrics in 11 or more variables, we prove an asymptotic for the number of rational points in an expanding box.

We construct several examples where duality transformation commutes with the orbifolding procedure even when the orbifolding group does not act freely, and there are massless states from the twisted sector at a generic point in the moduli…