8 problems

Tang–Kohmoto conjecture. An absolutely continuous spectrum is dominated by points with the trivial scaling index

Let $r$ denote a spatial scale, let $u$ be the kinematic viscosity, let $S{ij}$ be the strain-rate tensor, and let the energy dissipation field be $2nu S{ij}S{ij}$. Let $alpha$ be…

In turbulent flow, intense vorticity can generate local swirling regions, and transverse structure functions are especially sensitive to anti-aligned velocity vectors across vortex…

Fractional-moment multifractality conjecture. The same asymptotic extends to $h\in[0,1]$.

Let a random field satisfy a multifractal formalism, and suppose that its disorder-induced multifractality is subject to natural conditions. Fyodorov–Le Doussal–Rosso conjecture. T…

Let $X$ be the self-similar Lévy process considered in the paper, let ${}^q\!M_N^\tau(\omega)$ denote its empirical moment of order $q$ at scale $\tau$, and let $\nu_e(q)$ be the e…

Let $H$ be a random band matrix, let $\mathcal N(I)$ denote the smoothed number of eigenvalues in a mesoscopic interval $I$, and suppose that … Here $C_dW^{-d}$ is called the compr…

Let a many-body model with local interactions have a wave function represented in a natural basis, and let the number of particles vary. Generic multifractality conjecture. Multifr…