Related papers: Markovian loop clusters on the complete graph and …
An acyclic mapping from an $n$ element set into itself is a mapping $\phi$ such that if $\phi^k(x) = x$ for some $k$ and $x$, then $\phi(x) = x$. Equivalently, $\phi^\ell = \phi^{\ell+1} = ...$ for $\ell$ sufficiently large. We investigate…
The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…
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…
In this paper, we prove intractability results about sampling from the set of partitions of a planar graph into connected components. Our proofs are motivated by a technique introduced by Jerrum, Valiant, and Vazirani. Moreover, we use…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops ("loop soup") of parameter one-half associated to a transient symmetric Markov jump process on a network is half the square of the Gaussian free field on…
We study the number of chords and the number of crossings in the largest component of a random chord diagram when the chords are sparsely crossing. This is equivalent to studying the number of vertices and the number of edges in the largest…
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of…
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…
I tackle the problem of partitioning a sequence into homogeneous segments, where homogeneity is defined by a set of Markov models. The problem is to study the likelihood that a sequence is divided into a given number of segments. Here, the…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null…
A book embedding of a complete graph is a spatial embedding whose planar projection has the vertices located along a circle, consecutive vertices are connected by arcs of the circle, and the projections of the remaining "interior" edges in…
We present a general approach to study the flooding time (a measure of how fast information spreads) in dynamic graphs (graphs whose topology changes with time according to a random process). We consider arbitrary converging Markovian…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
We consider the almost semi-continuous processes defined on a finite Markov chain. The representation of the moment generating functions for the absolute maximum after achievement positive level and for the recovery time are obtained.…