Threshold phenomena are investigated using a general approach, following Talagrand [Ann. The general upper bound for the threshold width of symmetric monotone properties is improved. This follows… (More)

The QSAT problem is the quantified version of the SAT problem. We show the existence of a threshold effect for the phase transition associated with the satisfiability of random quantified extended… (More)

The theory of threshold phenomena can be traced back to [Russo, 1982], who described it as an “approximate zero-one law”(see also [Margulis, 1974], [Kahn et al., 1988] and [Talagrand, 1994]). These… (More)

Let N be distributed as a Poisson random set on R, d ≥ 2, with intensity comparable to the Lebesgue measure. Consider the Voronoi tiling of R, {Cv}v∈N , where Cv is composed of points x ∈ R that are… (More)

Take a big graph and make a random electrical network of it by assigning independent resistances on its edges. Now, ask for the behaviour of the effective resistance between two vertices (two… (More)

We investigate the threshold widths of some symmetric properties which range asymptotically between 1/ √ n and 1/ log n. These properties are built using a combination of failure sets arising from… (More)

We study the appearance of the giant component in random subgraphs of a given finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander… (More)