Related papers: Angle between two random segments
In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition,…
To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance…
Where are the intersection points of diagonals of a regular $n$-gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate these and related new questions in geometric probability,…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique…
In this work the dynamics of a freely jointed random chain with small masses attached to the joints is studied from a microscopic point of view. The chain is treated using a stringy approach, in which a statistical sum is performed over all…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…
In this thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\ldots X_{n},Y_{1},\ldots Y_{n}$ be $2n$ independent random variables, with uniform…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
We study site and bond percolation on directed simple random graphs with a given degree distribution and derive the expressions for the critical value of the percolation probability above which the giant strongly connected component emerges…
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
We consider a gas of point particles moving on the one-dimensional line with a hard-core inter-particle interaction that prevents particle crossings --- this is usually referred to as single-file motion. The individual particle dynamics can…
We consider random lines in $\mathbb{R}^3$ (random with respect to the kinematic measure) and how they intersect $\mathbb{S}^2$. It is known that the entry point and the exit point behave like \textit{independent} uniformly distributed…
The contact angle of a fluid droplet on an heterogeneous surface is analysed using the statistical dynamics of the spreading contact line. The statistical properties of the final droplet radius and contact angle are obtained through…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…