Related papers: The recombination equation for interval partitions
In the United States, regions are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can affect who's elected, and drawing districts to give an advantage to a certain group is known as…
Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. M\"ohle described the recursion which…
We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and,…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
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.…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
This work investigates the factorization of finite lattices to implode selected intervals while preserving the remaining order structure. We examine how complete congruence relations and complete tolerance relations can be utilized for this…
We propose a discrete lattice version of the Fokker-Planck kinetic equation along lines similar to the Lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension $D$. A generalized…
We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable through linearisation. We then introduce the general discrete…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
Initial boundary value problems for the generalized Benney-Lin equation posed on bounded intervals and on the right half-line were considered. The existence and uniqueness of global regular solutions on arbitrary intervals as well as their…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
The Nagumo lattice differential equation admits stationary solutions with arbitrary spatial period for sufficiently small diffusion rate. The continuation from the stationary solutions of the decoupled system (a system of isolated nodes) is…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration…
Matrix integrals used in random matrix theory for the study of eigenvalues of matrix ensembles have been shown to provide $ \tau $-functions for several hierarchies of integrable equations. In this paper, we construct the matrix integral…