10 problems

Let $\Lambda>1$ and let $\alpha\in(0,2)$. For each $\theta>0$, let $c_\theta$ denote the coefficient defined in Proposition corresponding to the asymptotics of the characteristic f…

Let $Z_t(F)$ be the functional of the derivative Gibbs measure associated with branching Brownian motion, and suppose that $F(x)\sim x^{-\alpha}$ as $x\to0$ for some $\alpha$ satis…

Total-length fluctuation conjecture. As $n\to\infty$,

Conjecture on the minimum. As $t\to\infty$, for some constant $C>0$,

Let $F(\beta,h)$ be the quenched free energy, let $h_c(\beta)$ be the critical point, and suppose the renewal inter-arrival law satisfies the regular-variation assumption and the e…

Let $\tau$ be the renewal process with inter-arrival law $K$, and let $h_c(\beta)$ denote the critical point at disorder intensity $\beta$. Assume that the environment satisfies th…

Consider randomly biased random walks on Galton–Watson trees without leaves, with exponent $\alpha\in(1,2)$, and assume a non-lattice condition. Stable-fluctuation conjecture. It w…

Consider randomly biased random walks on Galton–Watson trees without leaves, and impose a non-lattice condition on $\log A$, where $A$ is the random bias variable in the model. Sta…

Consider a $\beta$-biased random walk with exponent $\alpha\in(1,2)$, where $\alpha$ is defined at the paper's equation labelled $\alpha_{\mathrm{tree}}$. Let $\Delta_n$ denote the…

Let $Z_\alpha$ be a positive $\alpha$-stable random variable with $\alpha\in(0,1)$, and let $\gamma\in\mathbb{R}$. A positive random variable is generalized gamma convolution (GGC)…