相关论文: Random fractals and tree-indexed Markov chains

We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain…

We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…

We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…

This paper studies a number of matrix models of size n and the associated Markov chains for the eigenvalues of the models for consecutive n's. They are consecutive principal minors for two of the models, GUE with external source and the…

In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates.…

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…

We discuss the spectral asymptotics of some open subsets of the real line with random fractal boundary and of a random fractal, the continuum random tree. In the case of open subsets with random fractal boundary we establish the existence…

We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.

The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the…

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…

There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized,…

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…

This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…

We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a…

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 survey some of our recent results on the geometry of spatially independent martingales, in a more concrete setting that allows for shorter, direct proofs, yet is general enough for several applications and contains the well-known fractal…

The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…

One class of random walks with infinite memory, so called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We…

We consider a Bernoulli bond percolation on a random recursive tree of size $n\gg 1$, with supercritical parameter $p_n=1-c/\ln n$ for some $c>0$ fixed. It is known that with high probability, there exists then a unique giant cluster of…

We study here the small-angle scattering structure factor for deterministic fat fractals in the reciprocal space. It is shown that fat fractals are exact self-similar in the range of iterations having the same values of the scaling factor,…