Nodal set of monochromatic waves satisfying the Random Wave Model

We construct deterministic solutions to the Helmholtz equation in $\mathbb{R}^m$ which behave accordingly Random Wave Model. then find number of their nodal domains, volume and topologies nesting trees set growing balls around origin. The proof pseudo-random behaviour functions under consideration hinges on a de-randomisation technique pioneered by Bourgain proceeds via computing $L^p$-norms. study relies its stability properties evaluation doubling index, an average sense.