Related papers: Trees within trees II: Nested Fragmentations
The need to harmonise apparently irreconcilable arrangements in an ecosystem --nestedness and segregation-- has triggered so far different strategies. Methodological refinements, or the inclusion of behavioural preferences to the network…
Elucidating the interplay of defect and stress at the microscopic level is a fundamental physical problem that has strong connection with materials science. Here, based on the two-dimensional crystal model, we show that the instability mode…
The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation…
We provide explicit conditions, in terms of the transition kernel of its driving particle, for a Markov branching process to admit a scaling limit toward a self-similar growth-fragmentation with negative index. We also derive a scaling…
We consider a Markovian evolution on point processes, the $\Psi$--process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a…
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…
We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
The fragmentation processes of exchangeable partitions have already been studied by several authors. In this paper, we examine rather fragmentation of exchangeable compositions, that means partitions of $\mathbb{N}$ where the order of the…
Complex physical dynamics can often be modeled as a Markov jump process between mesoscopic configurations. When jumps between mesoscopic states are mediated by thermodynamic reservoirs, the time-irreversibility of the jump process is a…
A planar crack generically segments into an array of "daughter cracks" shaped as tilted facets when loaded with both a tensile stress normal to the crack plane (mode I) and a shear stress parallel to the crack front (mode III). We…
We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no…
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,…
The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of the…
We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables like current and activity pertain to the first class, which is composed by random variables that change whenever a jump in…
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…
The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…
Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Kingman (1978)'s representation theorem states that any exchangeable partition of $\mathbb{N}$ can be represented as a paintbox based on a random mass-partition. Similarly, any exchangeable composition (i.e. ordered partition of…