  In the first part of the paper, we solve the boundary and monodromy problems
for the isomonodromy equation of the $n\times n$ meromorphic linear system of
ordinary differential equations with Poncar\'{e} rank $1$. In particular, we
derive an explicit expression of the Stokes matrices of the linear system, via
the boundary value of the solutions of the isomonodromy equation at a critical
point. Motivated by this result, we then describe the regularized limits of
Stokes matrices as the irregular data $u={\rm diag}(u_1,...,u_n)$ in the linear
system degenerates, i.e., as some $u_i, u_j,...,u_k$ collapse. The prescription
of the regularized limit is controlled by the geometry of the De
Concini-Procesi wonderful compactification space. As applications, many
analysis problems about higher rank Painlev\'e transcendents can be solved.
  In the second part of the paper, we show some important applications of the
above analysis results in representation theory and Poisson geometry: we obtain
the first transcendental realization of crystals in representations of
$\frak{gl}_n$ via the Stokes phenomenon in the WKB approximation; we develop a
wall-crossing formula that characterizes the discontinuous jump of the
regularized limits of Stokes matrices as crossing walls in the compactification
space, and interpret the known cactus group actions on crystals arising from
representation theory as a wall-crossing phenomenon; and we find the first
explicit linearization of the standard dual Poisson Lie group for $U(n)$.
