Related papers: Scaling limits of the Schelling model
We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…
In this work, we propose and analyze a novel Schelling-type metapopulation model that examines how random relocations of families between neighborhoods can lead to segregation. The model consists of a large number of houses organized into…
We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An…
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic…
We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the…
The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article…
We consider a metapopulation version of the Schelling model of segregation over several complex networks and lattice. We show that the segregation process is topology independent and hence it is intrinsic to the individual tolerance. The…
We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
We consider a long-range interacting particle system in which binary particles -- whose initial states are chosen uniformly at random -- are located at the nodes of a flat torus $(\mathbb{Z}/h\mathbb{Z})^2$. Each node of the torus is…
We investigate the Schelling model of social segregation, formulated as an intrinsically non-equilibrium system, in which the agents occupy districts (or patches) rather than sites on a grid. We show that this allows the equations governing…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
Collective behaviour in biological systems pitches us against theoretical challenges way beyond the borders of ordinary statistical physics. The lack of concepts like scaling and renormalization is particularly grievous, as it forces us to…
We study occupancy counts for the critical nearest-neighbor branching random walk on the $d$-dimensional lattice, conditioned on non-extinction. For $d\geq 3$, Lalley and Zheng (2011) showed that the properly scaled joint distribution of…
We introduce a new lattice growth model, which we call boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass on $\mathbb{Z}^d$ ($d\geq 2$) onto the boundary of an (a priori) unknown domain. The…
Lattice gauge theories, discretized cousins of continuum gauge theories arising in the Standard Model, have become important platforms for exploring non-equilibrium quantum phenomena. Recent works have reported the possibility of…