Abstract. For super-heated water on a substrate with hydrophobic patches immersed in a hydrophilic matrix, one can choose the temperature so that micro-bubbles will form, grow and merge on the hydrophobic patches and not on the hydrophilic matrix. Until covering a patch, making a pinned...

We consider random walks Xn in Z+, obeying a detailed balance condition, with a weak drift towards the origin when Xn↗∞. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional Solid-On-Solid bridge with a corresponding Hamiltonian. Phase diagrams are...

The correlation structure of some remarkable point processes on the one-dimensional real line is investigated. More specifically, focus is on translation invariant determinantal, permanental and/or renewal point processes. In some cases, anomalous (non-Poissonian) fluctuations for the number of...

We compute the correlation function in the equilibrium version of Rényi's parking problem. The correlation length is found to diverge as 2−1π−2(1−ρ)−2 when ρ↗1 (maximum density) and as π−2(2ρ−1)−2 when ρ↘1/2 (minimum density).