Related papers: Persisting randomness in randomly growing discrete…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is…
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…
A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…
The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
In this paper we develop the elements of the theory of algorithmic randomness in continuous-time Markov chains (CTMCs). Our main contribution is a rigorous, useful notion of what it means for an individual trajectory of a CTMC to be random.…
In recent years there has been much progress in graph theory on questions of the following type. What is the threshold for a certain large substructure to appear in a random graph? When does a random graph contain all structures from a…
We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. The probability distribution of graphs of this kind is shown to depend on the…
This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite…
We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…