random-walks · Random walks & distributions · 6 records · all concepts
runs5
044The quantum reading of the intermediate cell (P-045) — the boundary as a quasicrystal, the bulk as a flat-band localizer — is either a transport signature or a decoration.run
045Run 044 sealed the graph Laplacian as the walk Hamiltonian, and on the Schreier graph the Laplacian cancels every loop — which is exactly where the graph's aperiodicity lives (which of b, c, d fixes a leaf follows the substitution).run
046Runs 044 and 045 walked the Grigorchuk Schreier graph under isotropic operators (the Laplacian, then the equal-weight Hecke operator) and found a ballistic path both times — every leaf carries exactly one loop, so equal weights make the loop potential constant and the operator periodic.run
047Run 046 found the Grigorchuk boundary walks like a quasicrystal under the anisotropic Hecke operator (β = 0.800) and run 044 found a random expander's walk saturates by t ≈ 2 and a path's is ballistic.run
088Run 044's bulk clause was confirmed — on the Grigorchuk level-4 coset graph the quantum walker stays near its origin at long times (PR/N = 0.096, return floor 76/N) against a random 4-regular graph's PR/N = 0.99 — and P-045 reads it as a transport signature of the intermediate-growth cell.run
probes1
P-045A quantum walk on the intermediate-growth cell — is the boundary a quasicrystal and the bulk a flat-band localizer, or is the analogy decorative?probe
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