相关论文: Scaling Limits for Minimal and Random Spanning Tre…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invariant under rotations, scalings, and, in the case of the MST,…

We study the fundamental question of how likely it is that two randomly chosen trees are isomorphic to each other for different models of random trees. We show that the probability decays exponentially for rooted labeled trees as well as…

We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…

We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…

Let $T$ be an infinite rooted tree with weights $w_e$ assigned to its edges. Denote by $m_n(T)$ the minimum weight of a path from the root to a node of the $n$th generation. We consider the possible behaviour of $m_n(T)$ with focus on the…

We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…

We consider Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We…

We consider loop-erased random walk (LERW) running between two boundary points of a square grid approximation of a planar simply connected domain. The LERW Green's function is the probability that the LERW passes through a given edge in the…

We investigate the space of consistent tree-level extensions of the maximal supergravities in ten dimensions. We parametrize theory space by the first few EFT coefficients and by the on-shell coupling of the lightest massive state, and…

It is well-known that the height profile of a critical conditioned Galton-Watson tree with finite offspring variance converges, after a suitable normalization, to the local time of a standard Brownian excursion. In this work, we study the…

A spanning tree $T$ in a graph $G$ is a sub-graph of $G$ with the same vertex set as $G$ which is a tree. In 1981, McKay proved an asymptotic result regarding the number of spanning trees in random $k$-regular graphs. In this paper we prove…

We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…

This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a graph which strongly preserves distances in the graph is a…

For a simple (unbiased) random walk on a connected graph with $n$ vertices, the cover time (the expected number of steps it takes to visit all vertices) is at most $O(n^3)$. We consider locally biased random walks, in which the probability…

We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results…

Permutons, which are probability measures on the unit square $[0, 1]^2$ with uniform marginals, are the natural scaling limits for sequences of (random) permutations. We introduce a $d$-dimensional generalization of these measures for all…

We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…

We study the asymptotic behavior of ``true" self-avoiding random walks on general infinite locally finite trees. In this model, the walk starts at the root and, at each step, from its current vertex chooses a neighboring edge to traverse…

In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to zeta(3)=1/1^3+1/2^3+1/3^3+... as n goes to infinity. We consider…