Related papers: Exponential Segregation in a Two-Dimensional Schel…
We present a complete analysis of the Schelling dynamical system [Haw2018] of two connected neighbourhoods, with or without population reservoirs, for different types of linear and nonlinear tolerance schedules. We show that stable…
The present work introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly-oriented rectangles. By conducting extensive simulations, we report high precision percolation thresholds for a variety of…
In his 1971's Dynamic Models of Segregation paper, the economist Thomas C. Schelling showed that a small preference for one's neighbors to be of the same color could lead to total segregation, even if total segregation does not correspond…
We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…
Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…
Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system…
We investigate the large-time behavior of the solutions of the two-dimensional Keller-Segel system in self-similar variables, when the total mass is subcritical, that is less than 8\pi after a proper adimensionalization. It was known from…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
Schelling's model of segregation demonstrates that even in the absence of social or governmental interventions, individuals with mild in-group preferences can self-organize into strongly segregated neighborhoods. Many variants of this…
Schelling's model of segregation looks to explain the way in which particles or agents of two types may come to arrange themselves spatially into configurations consisting of large homogeneous clusters, i.e.\ connected regions consisting of…
In theories with (sets of) two large extra dimensions and supersymmetry in the bulk, the presence of non-supersymmetric brane defects naturally induces a logarithmic potential for the volume of the transverse dimensions. Since the logarithm…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
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…
This paper is devoted to study a model of individual clustering with two specific reproduction rates in two space dimensions. Given q > 2 and an initial condition in W 1,q (\Omega), the local existence and uniqueness of solution have been…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
We study relaxation properties of two-body collisions in infinite spatial dimension. We show that this process exhibits multiscaling asymptotic behavior as the underlying distribution is characterized by an infinite set of nontrivial…
We study the behaviour of a Schelling-class system in which a fraction $f$ of spatially-fixed switching agents is introduced. This new model allows for multiple interpretations, including: (i) random, non-preferential allocation…
The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement…
Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. We introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and…