4 problems

For the Sine$_\beta$ point process at $\beta=2$, the two-point truncated correlation function is … A Berezinskii–Kosterlitz–Thouless transition conjecture. The critical value…

Lambert's conjecture. The $1/2$-Sobolev regularity condition is sufficient for the relevant convergence to the Gaussian distribution if and only if $\beta\le 2$.

Let $\rho_{\beta}^{(2)}(0,\lambda)$ denote the pair correlation function of the Sine-$\beta$ process, with $\beta>0$ and $\lambda$ the separation parameter. For even integer…

Maximum-deviation limit conjecture. There is a random variable $\xi$ such that