10 problems

Frisch–Parisi conjecture. In that Baire functional space, any typical element $f$ obeys some multifractal formalism and satisfies

Let $\theta_c$ be the critical parameter and let $\mathfrak S(\theta_c)$ denote the corresponding random set of points of slow growth. Write $\operatorname{\dim_{_{\rm H}}}$ for H…

Prevalent singularity spectrum conjecture. For every $f\in\widetilde{b}^{\mu,\Psi}_{p,q}([0,1]^d)$,

Let $u$ be a probability measure on $\mathbb{R}^d$, let $(\omega_k)_{k=1}^{\infty}$ be independent random points distributed according to $\nu$, and for $\alpha>0$ define … Write…

Spectrum equality conjecture. For a self-similar measure $\mu$ and all $t\in[t_{\min},t_{\max}]$,

Power-law spectrum conjecture. The moments of $M$ satisfy

Let $K\subset\mathbb{R}^{d}$ be a compact set, and let $\mathcal{M}(K)$ be the space of probability measures on $K$ with its weak topology. For a measure $\mu\in\mathcal{M}(K)$, wr…

Multifractal spectrum conjecture. For all $t \in [t_{\min},t_{\max}]$,

Return-time dimension conjecture. For a large class of dynamical systems,

Let $\bar\beta(t)$ denote the average spectrum of SLE, and let $t_{\min}$ and $t_{\max}$ be the two points such that a tangent to $\bar\beta(t)$ intersects the $y$-axis at $-1$. The…