Multifractality in finite-dimensional lattices

Investigate whether the partial-localization scenario generated by heterogeneous population growth with local stochastic resetting produces genuine multifractal fields when the model is defined on finite-dimensional lattices.

Background

The paper analyzes a mean-field model of heterogeneous multiplicative population growth with mean-field redistribution and independent Poissonian resetting. In the partially localized phase, rare reset-free growth episodes produce transient concentration on favorable sites, while the identity of the dominant sites continually changes within a subextensive pool. The resulting stationary fractions exhibit multifractal scaling.

The authors identify finite-dimensional lattices as the most important extension because spatial locality may substantially alter the competition between redistribution, heterogeneous growth, resetting, and leader turnover. It remains unresolved whether the mean-field multifractal behavior survives as a genuine spatially extended field rather than merely as a property of globally coupled site fractions.