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7 papers · 2 filters
Standard representation of multivariate functions on a general probability space
Svante Janson
It is well-known that a random variable, i.e., a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisti…
Graph limits and exchangeable random graphs
Persi Diaconis, Svante Janson
We develop a clear connection between deFinetti's theorem for exchangeable arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph limits (work of Lovasz and man…
The largest component in a subcritical random graph with a power law degree distribution
Svante Janson
It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent , the largest component is of order $n^{1/(γ-…
Tail estimates for the Brownian excursion area and other Brownian areas
Svante Janson, Guy Louchard
Several Brownian areas are considered in this paper: the Brownian excursion area, the Brownian bridge area, the Brownian motion area, the Brownian meander area, the Brownian double…
Line-of-sight percolation
Bela Bollobas, Svante Janson, Oliver Riordan
Given , let be the graph with vertex set in which two vertices are joined if they agree in one coordinate and differ by at most in the other. (Thus $Z…
Sorting using complete subintervals and the maximum number of runs in a randomly evolving sequence
Svante Janson
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial proble…