The rate-distortion saddle-point problem considered by Lapidoth (1997) consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random Gaussian codebook and minimum (Euclidean) distance encoding is employed. We extend Lapidoth’s analysis in several directions in this paper. Firstly, we consider refined asymptotics. In particular, when the sou...

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, qk(t), have the representation qk(t) = log det (I − λ Kk) − log det (I − λ Kk−1), where Kk are integral operators. This class includes the n-periodic cylindrical Toda equations. For n = 2 our results reduce to the previously computed asymptotics of the 2D radial sinh-Gordon equation ...

We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton– Watson process, as the sample size increases to infinity. The asymp-totics of additive functions of trees, such as sizes of trees and frequencies of types within trees, a higher-order asymptotic of the " relative frequency " estimator of the left eigenvector of the mea...

The paper develops the …xed-smoothing asymptotics in a two-step GMM framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic and the LM statistic remain asymptotically pivotal. I...

To continue a branch of homoclinic solutions starting from a Bogdanov–Takens (BT) point in parameter and state space, one needs a predictor based on asymptotics for the bifurcation parameter values and the corresponding small homoclinic orbits in the phase space. We derive two explicit asymptotics for the homoclinic orbits near a generic BT point. A recent generalization of the Lindstedt–Poinca...

We address a conjecture of D. Applebaum on small time trace asymptotics for subordinate Brownian motion on compact manifolds. In [1], heat trace asymptotics are computed for the semigroup of the square root of the Laplacian (the generator of the Cauchy process) on the n-dimensional torus, SU(2) and SO(3), and a conjecture is made [1, pp. 2493-2494] that such asymptotics should hold for all α-st...

Asymptotics and functional form of correlators in the XX-spin chain of finite length. Abstract We verify the functional form of the asymptotics of the spin-spin equal-time correlation function for the XX-chain, predicted by the hypothesis of conformal invariance at large distances and by the bosonization procedure. We point out that bosonization pocedure also predicts the functional form of the...

The radial (penny-shaped) model of hydraulic fracture is considered. tangential traction on the walls incorporated, including an updated evaluation energy release rate (fracture criterion), system asymptotics and need to account for stagnant zone formation near injection point. impact incorporating shear stress construction solvers, effectiveness approximating parameters using first term crack ...

We derive semiclassical asymptotics for the orthogonal polynomials P n (z) on the line with respect to the exponential weight exp(−NV (z)), where V (z) is a double-well quartic polynomial, in the limit when n, N → ∞. We assume that ε ≤ (n/N) ≤ λ cr − ε for some ε > 0, where λ cr is the critical value which separates orthogonal polynomials with two cuts from the ones with one cut. Simultaneously...