相关论文: Ultrametric and tree potential

We study distributions of meeting times for finite symmetric Markov chains. For Markov kernels defined on large state spaces which satisfy certain weak inhomogeneity in return probabilities of points up to large numbers of steps, we obtain…

There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such…

Phylogenetic trees constitute an interesting class of objects for stochastic processes due to the non-standard nature of the space they inhabit. In particular, many statistical applications require the construction of Markov processes on…

In arXiv:1609.05666v1 [math.PR] a functional limit theorem was proved. It states that symmetric processes associated with resistance metric measure spaces converge when the underlying spaces converge with respect to the…

In this paper we investigate the geometric properties of quasi-trees, and prove some equivalent criteria. We give a general construction of a tree that approximates the ends of a geodesic space, and use this to prove that every quasi-tree…

We make the first steps towards an understanding of the ergodic properties of a rational map defined over a complete algebraically closed non-archimedean field. For such a rational map R, we construct a natural invariant probability measure…

We consider a uniform spanning tree in a $\delta$-square grid approximation of a planar domain $\Omega$. For given integer $n\ge 2$, we condition the tree on the following $n$-arm event: we pick $n$ branches, emanating from $n$ points…

We study the watermelon probabilities in the uniform spanning forests on the two-dimensional semi-infinite square lattice near either open or closed boundary to which the forests can or cannot be rooted, respectively. We derive universal…

We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree…

We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…

In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the…

We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant…

A mated-CRT map is a random planar map obtained as a discretized mating of correlated continuum random trees. Mated-CRT maps provide a coarse-grained approximation of many other natural random planar map models (e.g., uniform triangulations…

We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…

Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…

We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…

We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…

In this paper, we aim to provide probabilistic and combinatorial insights into tree formulas for the Green function and hitting probabilities of Markov chains on a finite state space. These tree formulas are closely related to loop-erased…

We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of…