Related papers: Local limit of the fixed point forest

We investigate a class of growing graphs embedded into the $d$-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on…

Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…

The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data…

We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method. Our estimates only involve first and second order difference operators and are closely…

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 prove rigorously several results about the site-percolation on random recursive trees, observed in the previous work by Kalay and Ben-Naim [J. Phys. A48(2015), no.4, 0405001, 15 pp.]. For a random recursive tree of size $n$, let every…

Given the high computational complexity of decision tree estimation, classical methods construct a tree by adding one node at a time in a recursive way. To facilitate promoting fairness, we propose a fairness criterion local to the tree…

Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…

Tracking the movement of tracer particles has long been a strategy for uncovering complex structures. Here, we study discrete-time random walks on finite Cayley trees to infer key parameters such as tree depth and geometric bias toward the…

We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…

We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite paths and the sphere with radius $r$ grows…

We are interested in estimating the location of what we call "smooth change-point" from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from…

A permutation can be locally classified according to the four local types: peaks, valleys, double rises and double falls. The corresponding classification of binary increasing trees uses four different types of nodes. Flajolet demonstrated…

This paper focuses on the size-biased permutation of $n$ independent and identically distributed (i.i.d.) positive random variables. This is a finite dimensional analogue of the size-biased permutation of ranked jumps of a subordinator…

We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…

Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones,…

While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…

As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the…

We study $I(T)$, the number of inversions in a tree $T$ with its vertices labeled uniformly at random, which is a generalization of inversions in permutations. We first show that the cumulants of $I(T)$ have explicit formulas involving the…

Given a graph $G=(V,E)$ with arboricity $\alpha$, we study the problem of decomposing the edges of $G$ into $(1+\epsilon)\alpha$ disjoint forests in the distributed LOCAL model. Barenboim and Elkin [PODC `08] gave a LOCAL algorithm that…