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1.
Summary We discuss statistical properties of random walks conditioned by fixing a large area under their paths. We prove the functional central limit theorem (invariance principle) for these conditional distributions. The limiting Gaussian measure coincides with the conditional probability distribution of certain timenonhomogeneous Gaussian random process obtained by an integral transformation of the white noise. From the point of view of statistical mechanics the studied problem is the problem of describing the fluctuations of the phase boundary in the one-dimensional SOS-model. 相似文献
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3.
We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups
and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup exp(G)\exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G). 相似文献
4.
We discuss some statistical properties of the phase boundary in the 2D low-temperature Ising ferromagnet in a box with the
two-component boundary conditions. We prove the weak convergence in C[0,1] of measures describing the fluctuations of phase boundaries in the canonical ensemble of interfaces with fixed endpoints
and area enclosed below them. The limiting Gaussian measure coincides with the conditional distribution of certain Gaussian
process obtained by the integral transformation of the white noise.
Received: 20 July 1996 / Accepted: 18 February 1997 相似文献
5.
Let A be a self-adjoint operator in a Krein space
Under certain natural assumptions, it is shown precisely which real eigenvalues of A can be given a max-inf characterization generalizing the usual one in Hilbert space. This result unifies several approaches in the recent literature. 相似文献
6.
We derive eigenvalue asymptotics for Sturm-Liouville operators with singular complex-valued potentials from the space , α∈[0,1], and Dirichlet or Neumann-Dirichlet boundary conditions. We also give application of the obtained results to the inverse spectral problem of recovering the potential from these two spectra. 相似文献
7.
In this paper behaviour of the spectrum of matrix-valued functions depending analytically on two parameters is studied. Generalizations of the Rellich theorem on analytic dependence of the spectrum and complete regular splitting of multiple eigenvalues are established.This work is partially supported by Natural Sciences and Engineering Research Council of Canada. R. H. also acknowledges appointment as a Post Doctoral Fellow of the Pacific Institute for Mathematical Sciences. 相似文献
8.
We study the problem of factorisation of non-negative Fredholm operators acting in the Hilbert space L2(0, 1) and its relation to the inverse spectral problem for Bessel operators. In particular, we derive an algorithm of reconstructing
the singular potential of the Bessel operator from its spectrum and the sequence of norming constants. 相似文献
9.
Let S be the multiplication operator by an independent variable x in L
2(0,1), and let V be an integral operator of Volterra type. In this note, we find sufficient conditions for the similarity of the operators T := S + V and S and discuss some generalizations to an abstract setting of the results obtained. 相似文献
10.
We solve the inverse spectral problem of recovering the singular potential from W−12(0,1) of a Sturm-Liouville operator by its spectra on the three intervals [0,1], [0,a], and [a,1] for some a∈(0,1). Necessary and sufficient conditions on the spectral data are derived, and uniqueness of the solution is analyzed. 相似文献