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These notes survey the first and recent results on large deviations of Schramm-Loewner evolutions (SLE) with the emphasis on interrelations among rate functions and applications to complex analysis. More precisely, we describe the large deviations of SLE$_kappa$ when the $kappa$ parameter goes to zero in the chordal and multichordal case and to infinity in the radial case. The rate functions, namely Loewner and Loewner-Kufarev energies, are closely related to the Weil-Petersson class of quasicircles and real rational functions.
Let $D={mathbb H}setminus bigcup_{j=1}^N C_j$ be a standard slit domain, where ${mathbb H}$ is the upper half plane and $C_j,1le jle N,$ are mutually disjoint horizontal line segments in ${mathbb H}$. A stochastic Komatu-Loewner evolution denoted by
We derive the large deviation principle for radial Schramm-Loewner evolution ($operatorname{SLE}$) on the unit disk with parameter $kappa rightarrow infty$. Restricting to the time interval $[0,1]$, the good rate function is finite only on a certain
In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE($kappa,rho_c$). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we o
The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying only confo
Let $X^{(delta)}$ be a Wishart process of dimension $delta$, with values in the set of positive matrices of size $m$. We are interested in the large deviations for a family of matrix-valued processes ${delta^{-1} X_t^{(delta)}, t leq 1 }$ as $delta$