Ideal-gas like market models with savings: quenched and annealed cases

Discontinuous phase transitions in the multi-state noisy $q$-voter model: quenched vs. annealed disorder

We introduce a generalized version of the noisy $q$-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $s \ge 2$ states. As in the original binary $q$-voter model, which corresponds to $s=2$, at each update randomly selected voter can conform to its $q$ randomly chosen neighbors (copy their state) only if all $q$ neighbors are in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act indep…

Nonlinear $q$-voter model from the quenched perspective

We compare two versions of the nonlinear $q$-voter model: the original one, with annealed randomness, and the modified one, with quenched randomness. In the original model, each voter changes its opinion with a certain probability $ε$ if the group of influence is not unanimous. In contrast, the modified version introduces two types of voters that act in a deterministic way in case of disagreement in the influence group: the fraction $ε$ of voters always change their current opinion, whereas the rest of them always maintain it. Although both concepts of randomness lead to the same average numbe…

Pair approximation for the q-voter models with quenched disorder on networks

Using two models of opinion dynamics, the $q$-voter model with independence and the $q$-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. To derive phase diagrams on networks, we develop the pair approximation for the quenched versions of the models. This formalism can be also applied to other quenched dynamics of similar kind. The results indicate that such a change of disorder eliminates all discontinuous phase transitions and broadens ordered phases. We show that although the annealed and quenched types of…

异质网络模型的确定性、淬火与退火参数估计

Deterministic, quenched and annealed parameter estimation for heterogeneous network models

本文针对连续条件异质网络模型，比较确定性、淬火式与退火式参数估计，证明退火估计是确定性方法的最佳替代。

Detailed simulation results for some wealth distribution models in Econophysics

In this paper we present detailed simulation results on the wealth distribution model with quenched saving propensities. Unlike other wealth distribution models where the saving propensities are either zero or constant, this model is not found to be ergodic and self-averaging. The wealth distribution statistics with a single realization of quenched disorder is observed to be significantly different in nature from that of the statistics averaged over a large number of independent quenched configurations. The peculiarities in the single realization statistics refuses to vanish irrespective of wh…

当群体多样性何时重要？二选一动态的统一框架

When Does Population Diversity Matter? A Unified Framework for Binary-Choice Dynamics

本文提出一个统一框架，研究二选一动态中群体多样性对集体行为的影响，并通过转换概率约束条件揭示淬火动态与退火动态的等价性。