Mikhail Isaev

New Global Stability Estimates for Monochromatic Inverse Acoustic Scattering

We give new global stability estimates for monochromatic inverse acoustic scattering. These estimates essentially improve estimates of [P. Hahner, T. Hohage, SIAM J. Math. Anal., 33 (2001), pp. 670...

Energy- and Regularity-Dependent Stability Estimates for Near-Field Inverse Scattering in Multidimensions

We prove new global Holder-logarithmic stability estimates for the near-field inverse scattering problem in dimension . Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimension is also given.

Asymptotic behavior of the number of Eulerian orientations of graphs

The class of simple graphs with large algebraic connectivity (the second minimal eigenvalue of the Laplacian matrix) is considered. For graphs of this class, the asymptotic behavior of the number of Eulerian orientations is obtained. New properties of the Laplacian matrix are established, as well as an estimate of the conditioning of matrices with asymptotic diagonal dominance is obtained.

Complex martingales and asymptotic enumeration

Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic behaviour of such integrals, we establish explicit bounds on the exponentials of complex martingales. Those bounds applied to the case of truncated normal distributions are precise enough to include and extend many enumerative results of Barvinok, Canfield, Gao, Greenhill, Hartigan, Isaev, McKay, Wang, Wormald, and others. Our method applies to sums as well as integrals. As a first illustration of the power of our theory, we considerably strengthen existing results on the relationship between random graphs or bipartite graphs with specified degrees and the so-called

On a bound of Hoeffding in the complex case

\beta

Exponential instability in the Gel'fand inverse problem on the energy intervals

-model of random graphs with independent edges, which is equivalent to the Rasch model in the bipartite case.

Energy and regularity dependent stability estimates for the Gel'fand inverse problem in multidimensions

It was proved by Hoeffding in 1963 that a real random variable X confined to [a, b] satisfies E e^(X--E X)

Exponential Instability in the Inverse Scattering Problem on the Energy Interval

\le

Stability estimates for determination of potential from the impedance boundary map

e^((b--a)^2/8). We generalise this to complex random variables.