Related papers: Scaling limits of the Schelling model
Schelling's segregation model is a landmark model in sociology. It shows the counter-intuitive phenomenon that residential segregation between individuals of different groups can emerge even when all involved individuals are tolerant.…
The Schelling model of segregation between two groups of residential agents (Schelling 1971; Schelling 1978) reflects the most abstract view of the non-economic forces of residential migrations: be close to people of 'your own'. The model…
Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling…
This paper generalizes the original Schelling (1969, 1971a,b, 2006) model of racial and residential segregation to a context of variable externalities due to social linkages. In a setting in which individuals' utility function is a convex…
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…
The phenomenon of residential segregation was captured by Schelling's famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same…
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…
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 first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Urban segregation of different communities, like blacks and whites in the USA, has been simulated by Ising-like models since Schelling 1971. This research was accompanied by a scientific segregation, with sociologists and physicists…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
The usual thermodynamic limit for systems of classical self-gravitating point particles becomes well defined, as a {\it dynamical} problem, using a simple physical prescription for the calculation of the force, equivalent to the so-called…
We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
We model the dynamics of the Schelling model for agents described simply by a continuously distributed variable - wealth. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the…
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying…
We consider the constrained Schelling model of social segregation in which the utility factor of agents strictly increases and non-local jumps of the agents are allowed. In the present study, the utility factor u is defined in a way such…
The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions,…
We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection…
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…