相关论文: Inverse problems for random walks on trees: networ…

Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…

We say that a vertex $v$ in a connected graph $G$ is decisive if the numbers of walks from $v$ of each length determine the graph $G$ rooted at $v$ up to isomorphism among all connected rooted graphs with the same number of vertices. On the…

We consider the first-passage percolation problem on the random graph with vertex set N\times{0,1}, edges joining vertices at Euclidean distance equal to unity and independent exponential edge weights. We provide a central limit theorem for…

We consider an inverse problem in information diffusion modeled by random walks on combinatorial graphs. The problem concerns reconstruction of vertex centrality from the distribution of the first passage times observed on a subset of…

This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…

Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…

The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…

We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…

For a graph $G$, let $t(G)$ denote the maximum number of vertices in an induced subgraph of $G$ that is a tree. Further, for a vertex $v\in V(G)$, let $t^v(G)$ denote the maximum number of vertices in an induced subgraph of $G$ that is a…

The 1-2-3 Conjecture, introduced by Karo\'nski, {\L}uczak, and Thomason in 2004, was recently solved by Keusch. This implies that, for any connected graph $G$ different from $K_2$, we can turn $G$ into a locally irregular multigraph $M(G)$,…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…

We present a new and surprisingly simple analysis of random-shift decompositions -- originally proposed by Miller, Peng, and Xu [SPAA'13]: We show that decompositions for exponentially growing scales $D = 2^0, 2^1, \ldots,…

We provide a new approach for proving the indistinguishability of connected components of random one-or-two-ended oriented forests on unimodular random graphs. In particular, this approach leads to a new and simpler proof for the wired…

We show that for any fixed dense graph G and bounded-degree tree T on the same number of vertices, a modest random perturbation of G will typically contain a copy of T . This combines the viewpoints of the well-studied problems of embedding…

Consider the d-dimensional lattice Z^d where each vertex is ``open'' or ``closed'' with probability p or 1-p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth co-ordinates of v and w…

We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…

We study the inverse problem of determining the conductivity matrix of an electrical network from the prescribed knowledge of the magnitude of the induced current along the edges coupled with the imposed voltage or injected current on the…

The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…

In the United States, regions are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can affect who's elected, and drawing districts to give an advantage to a certain group is known as…

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…