Let $X_{t}=\sum_{i=1}^n(1+s\cdot w)\sin(t_i)$ where $t\in T=[-\pi/2,\pi/2]^n/\{\vec 0\}$, $w\sim\mathbb{N}(0,1)$, $s$ is a scalar denoting the strength of Gaussian noise. How to find the condition on $s$ such that $X_t$ is strictly positive with high probability? i.e. when $n\rightarrow\infty$,

$$P(\inf X_t>0)\rightarrow 1.$$