7 problems

The circular block-maxima method and the disjoint block-maxima method are considered under a suitable triangular-array structure. Variance-advantage conjecture. The advantages of t…

Gumbel-fluctuation conjecture. After an appropriate choice of ${\cal C}$, the proposed transformation of $\lambda_{\max}$ continues to have a Gumbel distribution. The conjecture ex…

Let $x_{\max}(t)$ denote the maximum position attained by the branching run-and-tumble particle process up to time $t$, and let $t_{\max}$ be the time at which this maximum is reac…

Weiss–Shuler–Lindenberg conjecture. The expected $k$-th extreme first-passage time satisfies

Let $\rho_n$ denote the smallest modulus among the roots of the degree-$n$ complex Kac polynomial, and let $x>0$. The transition regime is obtained by evaluating the event…

Let $\beta_N$ be a sequence tending to $0$ as $N\to\infty$, and let $\lambda_0^N$ denote the largest eigenvalue of the matrix $X_N$. In the regime where $\beta_N$ decreases faster…

Log-correlated Gaussian fields are Gaussian fields whose correlations decay logarithmically with distance; their extreme-value statistics are expected to resemble those of independ…