Minimal coupling density preserving SYK chaos in sparse models
In plain words
Removing most random couplings from SYK makes it easier to simulate on quantum hardware. It is unclear how many couplings can be removed before it stops behaving like a black hole.
Precise statement
In sparse Majorana SYK with $N$ fermions and $k$ $N$ four-body terms chosen at random, find the critical $k_c$ (as $N\to\infty$) below which the low-temperature Schwarzian regime and near-maximal Lyapunov exponent are lost, and the $1/k$ corrections above it. Answer: $k_c$, or the scaling of physical quantities with $k$.
What would settle it
An analytic large-N treatment of sparse random hypergraphs plus large-N numerics of spectra and OTOCs at several k.
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