358 research outputs found
Random Metric Spaces and Universality
WWe define the notion of a random metric space and prove that with
probability one such a space is isometricto the Urysohn universal metric space.
The main technique is the study of universal and random distance matrices; we
relate the properties of metric (in particulary universal) space to the
properties of distance matrices. We show the link between those questions and
classification of the Polish spaces with measure (Gromov or metric triples) and
with the problem about S_{\infty}-invariant measures in the space of symmetric
matrices. One of the new effects -exsitence in Urysohn space so called
anarchical uniformly distributed sequences. We give examples of other
categories in which the randomness and universality coincide (graph, etc.).Comment: 38 PAGE
On the limiting power of set of knots generated by 1+1- and 2+1- braids
We estimate from above the set of knots, , generated by
closure of n-string 1+1- and 2+1-dimensional braids of irreducible length
() in the limit n>>1.Comment: 14 LaTeX pages, 2 PostScript figure
The Basic Representation of the Current Group O(n,1)^X in the L^2 space over the generalized Lebesgue Measure
We give the realization of the representation of the current group O(n,1)^X
where X is a manifold, in the Hilbert space of L^2(F,\nu) of functionals on the
the space F of the generalized functions on the manifold X which are square
integrable over measure \nu which is related to a distinguish Levy process with
values in R^{n-1} which generalized one dimensional gamma process. Unipotent
subgroup of the group O(n,1)^X acts as the group of multiplicators. Measure \nu
is sigma-finite and invariant under the action current group O(n-1)^X. Ther
case of n=2 (SL(2,R^X)) was considered before in the series of papers starting
from the article Vershik-Gel'fand-Graev (1973).Comment: 26 p. Refs 1
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