Related papers: Random Young diagrams in a Rectangular Box
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the…
Consider a family of random ordinary differential equations on a manifold driven by vector fields of the form $\sum_kY_k\alpha_k(z_t^\epsilon(\omega))$ where $Y_k$ are vector fields, $\epsilon$ is a positive number, $z_t^\epsilon$ is a…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law). Then we prove that the law of the radial part of…
We introduce a two-dimensional, distribution-valued field which we call the quadratic field associated to the one-dimensional Ornstein-Uhlenbeck process. We show that the stationary quadratic fluctuations of the simple exclusion process,…
Let G be a vertex transitive graph. A study of the range of simple random walk on G and of its bridge is proposed. While it is expected that on a graph of polynomial growth the sizes of the range of the unrestricted random walk and of its…
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state.…
In this paper we consider the Erd\H{o}s-R\'enyi random graph in the sparse regime in the limit as the number of vertices $n$ tends to infinity. We are interested in what this graph looks like when it contains many triangles, in two…
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic…
The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
We show that quantum fields confined to Lorentzian histories of freely falling networks in Minkowski spacetime probe entanglement properties of vacuum fluctuations that extend unrestricted across spacetime regions. Albeit instantaneous…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…
A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary,…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.