1,001,641 research outputs found
Uniform random colored complexes
We present here random distributions on -edge-colored, bipartite
graphs with a fixed number of vertices . These graphs are dual to
-dimensional orientable colored complexes. We investigate the behavior of
quantities related to those random graphs, such as their number of connected
components or the number of vertices of their dual complexes, as . The techniques involved in the study of these quantities also yield a
Central Limit Theorem for the genus of a uniform map of order , as .Comment: 36 pages, 9 figures, minor additions and correction
Averaging along Uniform Random Integers
Motivated by giving a meaning to "The probability that a random integer has
initial digit d", we define a URI-set as a random set E of natural integers
such that each n>0 belongs to E with probability 1/n, independently of other
integers. This enables us to introduce two notions of densities on natural
numbers: The URI-density, obtained by averaging along the elements of E, and
the local URI-density, which we get by considering the k-th element of E and
letting k go to infinity. We prove that the elements of E satisfy Benford's
law, both in the sense of URI-density and in the sense of local URI-density.
Moreover, if b_1 and b_2 are two multiplicatively independent integers, then
the mantissae of a natural number in base b_1 and in base b_2 are independent.
Connections of URI-density and local URI-density with other well-known notions
of densities are established: Both are stronger than the natural density, and
URI-density is equivalent to log-density. We also give a stochastic
interpretation, in terms of URI-set, of the H_\infty-density
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