20 problems

Archimedes configurations. For all $t\in(0,1)$, the scaled configuration converges in distribution to the Archimedes measure in the vague topology for random Borel measures on…

Let $\mu_{\mathrm{ISE}}$ be the integrated superBrownian excursion measure on $\mathbb{R}$, and let $Y(\lambda)$ be the non-negative random variable whose law is specified by the l…

Transport-distance finiteness conjecture. If $\Phi$ is $(p+\vartheta)$-uniform for some $\vartheta>0$, then

Red-leaf empirical-measure conjecture. Under $\mathbb{P}_{x_t}$, this random measure converges in law for the topology of vague convergence, and its limiting law does not depend on…

Density conjecture. Real-valued QID random measures are dense in the space of independently scattered real-valued random measures, regarded as random elements of…

Exponential concentration conjecture. There exist constants $c_1,c_2>0$ such that, for every $n$,

Angel–Holroyd–Romik–Virág Archimedean-limit conjecture. For every $t\in[0,1]$,

Let $\Phi[\sigma;1;f]$ be the limiting object considered in the paper, and let $(\mathfrak l_{k_h})_h$ be the system of dynamical symmetry Lie algebras associated with the embeddin…

Morris distribution conjecture.

Selberg distribution conjecture. Its distribution has Mellin transform

Let $M$ be a surface of genus ${\bf g}$, let $\mathcal{T}_{N,\mathbf{g}}$ denote the set of triangulations of size $N$, and let $\nu_a$ be the random measure defined by … for posit…

Let $\mathfrak D$ be the class of domains in the source, let $D_N$ be the corresponding lattice approximation, let $h_z$ be the discrete Gaussian free field, let $m_N$ be its cente…

Let $G_N$ be the Gibbs measures of a mixed $p$-spin glass model on the hypercube with zero external field. The model admits an Orthogonal Structure if there is a sequence…

Inner phase II conjecture. The following convergence in law holds:

Supercritical renormalization conjecture. As $\varepsilon\to0$,

Let $\alpha e0$ and let $\gamma^2trianglelefteq2d$ describe the parameters in the lognormal star-scale invariant setting; $M$ denotes a solution random measure. **Solutions conjectur…

Let $\tilde{\Omega}$ be the space of equivalence classes of SLE(2) curves in $\mathbb{D}$, let $\mathcal{M}$ be the relevant space of measures, and let $G(z)=G_{\mathbb{D}}(z)$ den…

For a fixed interval $[a,b]$, let $\mathsf{\overline{\mu}}_r[a,b]$ be the finite-radius approximations to the local-time measure and let $\mathsf{\overline{\mu}}[a,b]$ denote their…

Let $\rho\trimmed$ be a stationary random measure on $\mathbb{R}$ with intensity-one asymptotic density, let $\mathscr{K}$ be the disjoint union of…

Lagrangian measure convergence conjecture. The measures ${\bf Q}_{r,t}$ converge to a random measure ${\bf Q}_r$ on $D_1\setminus{\mathcal B}(0,r)$ as $t\to\infty$, in the sense of…