Aging effects in Schelling segregation model

Abstract

The Schelling model has become a paradigm in social sciences to explain the emergence of residential spatial segregation, even in the presence of high tolerance to mixed neighborhoods by the side of citizens. In particular, we consider a noisy constrained version of the Schelling model, in which agents maximize its satisfaction, related to the composition of the local neighborhood, by infinite-range movements towards satisfying vacancies. We add to it an aging effect by making the probability of agents to move inversely proportional to the time they have been satisfied in their present location. This mechanism simulates the development of an emotional attachment to a location where an agent has been satisfied for a while. The introduction of aging has several major impacts on the model statics and dynamics: the phase transition between a segregated and a mixed phase of the original model disappears, and we observe segregated states with a high level of agent satisfaction even for high values of tolerance. In addition, the new segregated phase is dynamically characterized by a slow power-law coarsening process similar to a glassy-like dynamics.

Ordering dynamics and aging in the symmetrical threshold model

“…The key finding is that the mixed phase (phase I), characterized by an asymptotically disordered dynamically active state, does not always exist: the aging mechanism can drive the system to an asymptotic absorbing ordered state, regardless of how low the threshold T is set. A similar effect of aging was already described for the Schelling model in [41]. When the dynamics are examined in detail, a new phase I * , defined in terms of dynamical properties, emerges in the domain of parameters where the model without aging displays phase I.…”

“…Aging refers to the property of agents becoming less likely to change their state the longer they have remained in that state [33,[37][38][39][40][41][42]46]. In contrast to the original model, which assumes that agents update their state at a constant rate, this model introduces an activation function p A (j) that is inversely proportional to the agent's internal time j.…”

“…Following previous literature on aging effects [30,34,39,41,42] we make the choice of p A (j) = 1/(j + 2) for the aging probability. This particular choice is motivated by the fact that it allows to reproduce inter-event time distributions observed empirically [44,46].…”

“…As such, the longer an agent remains in the current state, the smaller the probability of changing. Aging has been shown to cause coarsening dynamics toward a consensus state in the Voter model [34,38], to induce bona fide continuous phase transitions in the noisy Voter model [39,40], modify the phase diagram and non-equilibrium dynamics of the Schelling segregation model [41], and to modify non-trivially the cascade dynamics of the threshold model [42]. The introduction of aging is motivated by strong empirical evidence that human interactions do not occur at a constant rate and cannot be described using a Markovian assumption.…”

Aging in Some Opinion Formation Models: A Comparative Study

“…Initially termed as "inertia" [25], it was shown that the slowing down of the microscopic dynamics induced via aging actually decreased the time needed to reach the macroscopically ordered state state of consensus. In this respect, and in alignment with previous studies [25][26][27][28][29][30][31], we consider that aging acts on the mechanism associated with social contagion.…”