term of the asymptotic formula confirms the so-called Forrester-Chen-Eriksen-Tracy conjecture [@CET95; @Forrester93]. This conjecture asserts that if the density of state behaves as $|x-x^*|^\beta$ near a point $x^*$, then the probability $E(s)$ of emptiness of the interval $(x^* -s, x^* +s)$ behaves like $$E(s) \sim  \exp \biggl(-C s^{2\beta +2} \biggr), \qquad \textrm{as } s \to +\infty.$$ In the present Pearcey case, we have $\beta = \frac{1}{3}$ and $2\beta +2 = \frac83$.

Evaluation of the constant $C$ in is a challenging problem in the studies of large gap asymptotics [@Kra1]. For the classical sine, Airy and Bessel kernels encountered in random matrix theory, one could resolve this problem either by investigating the relevant Hankel or Toeplitz determinants which approximate the Fredholm determinants [@DIK2008; @DIKZ; @dkv; @Kra2], or by studying the total integrals of the Painlevé transcendents on account of Tracy-Widom type formulas for the gap probability [@BRD08]; see also [@BE; @E10; @E06] for the approach of operator theory. It seems unlikely that these methods are applicable in the present case. One rough idea to tackle this problem is based on the observation that, as the parameter $\rho$ tends to $-\infty$, the cusp singularity at the origin disappears and the origin becomes 