6 problems

Consider the Matheron–de Marsily model, a random walk $(M_n)_{n\in\mathbb N}$ in a randomly oriented lattice on $\mathbb Z^2$, and let its survival probability be the probability t…

Let $H\in(0,1)$ and let $B^H$ be fractional Brownian motion. Define the integrated fractional Brownian motion by … Its persistence probability has polynomial asymptotics with persi…

Let $\theta(\ell)$ be the persistence decay exponent appearing in the fixed-$\ell$ persistence asymptotic, with $\ell$ a positive integer. Large-size persistence exponent conjectur…

Spectral gap conjecture. The persistence should satisfy

Persistence exponent conjecture. The persistence exponent should be

Persistence exponent conjecture. For any such walk,