Near-critical percolation in two dimensions.
Near-minimal spanning trees : a scaling exponent in probability models
We study the relation between the minimal spanning tree (MST) on many random points and the “near-minimal” tree which is optimal subject to the constraint that a proportion δ of its edges must be different from those of the MST. Heuristics suggest that, regardless of details of the probability model, the ratio of lengths should scale as 1+Θ(δ2). We prove this scaling result in the model of the lattice with random edge-lengths and in the euclidean model.
Non equilibrium fluctuations for a zero range process
Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles.
Nonequilibrium central limit theorem for a tagged particle in symmetric simple exclusion
Nonequilibrium fluctuations for a tagged particle in one-dimensional sublinear zero-range processes
Nonequilibrium fluctuations of a tagged, or distinguished particle in a class of one dimensional mean-zero zero-range systems with sublinear, increasing rates are derived. In Jara–Landim–Sethuraman (Probab. Theory Related Fields145 (2009) 565–590), processes with at least linear rates are considered. A different approach to establish a main “local replacement” limit is required for sublinear rate systems, given that their mixing properties are much different. The method discussed also allows to...
Non-intersecting, simple, symmetric random walks and the extended Hahn kernel
We show using non-intersecting paths, that a random rhombus tiling of a hexagon, or a boxed planar partition, is described by a determinantal point process given by an extended Hahn kernel.
Nonlinear diffusion with jumps
Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes
Doubly stochastic point processes driven by non-Gaussian Ornstein–Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.
Nonlinear Markov processes in big networks
Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly,...
Nonmonotonic coexistence regions for the two-type Richardson model on graphs.
Non-perturbative approach to random walk in Markovian environment.
Nucleation for a long range magnetic model
Nucleation parameters for discrete threshold growth on .