Related papers: A geometric representation of fragmentation proces…
To model the destruction of a resilient network, Cai, Holmgren, Devroye and Skerman introduced the $k$-cut model on a random tree, as an extension to the classic problem of cutting down random trees. Berzunza, Cai and Holmgren later proved…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
Growth-fragmentation processes describe the evolution of systems in which cells grow slowly and fragment suddenly. Despite originating as a way to describe biological phenomena, they have recently been found to describe the lengths of…
We develop two approaches to the problem of soft fragmentation of hadrons in a gauge theory for high energy processes. The first approach directly adapts the standard resummation of the parton distribution function's anomalous dimension…
Can we obtain a Brownian CRT of mass $1/2$ from a CRT of mass $1$ by cutting certain branches? In this paper, we will answer that question in the much more general setting of self-similar Markov trees. Self-similar Markov trees (ssMt) are…
Theories suggest that filament fragmentation should occur on a characteristic fragmentation length-scale. This fragmentation length-scale can be related to filament properties, such as the width and the dynamical state of the filament. Here…
For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees…
The Littlewood decomposition for partitions is a well-known bijection between partitions and pairs of $t$-core and $t$-quotient partitions. This decomposition can be described in several ways, such as the $t$-abacus method of James or the…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Parton fragmentation functions (FFs) are indispensable for understanding processes of hadron production ubiquitously existing in high-energy collisions, but their first principle determination has never been realized due to the…
We study random trees which are invariant in law under the operation of contracting each edge independently with probability $p\in(0,1)$. We show that all such trees can be constructed through Poissonian sampling from a certain class of…
We study the bounded regions in a generic slice of the hyperplane arrangement in $\mathbb{R}^n$ consisting of the hyperplanes defined by $x_i$ and $x_i+x_j$. The bounded regions are in bijection with several classes of combinatorial…
We show that branched coverings of surfaces of large enough genus arise as characteristic maps of braided surfaces that is, lift to embeddings in the product of the surface with $\mathbb R^2$. This result is nontrivial already for…
Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…
We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demon- strate how this setting encompasses arbitrary weighted…
Consider the Markov process taking values in the partitions of N such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate d. This is a special case of exchangeable…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
Parametrizations of fragmentation functions (FFs) from $e^+$-$e^-$ and p-\=p collisions are combined with a parton spectrum model in a pQCD folding integral to produce minimum-bias {\em fragment distributions}. A model of in-medium FF…