Request for recommendation in probability and complex analysis Could somebody kindly recommend to me some books which deal with the applications of the probabilistic method to problems in real and complex analysis or which consider probabilistic versions of some problems in real and complex analysis?  I would also like to know about some books/resources dealing with applications of complex analysis to the theory of probability.  I would be highly obliged.
 A: A classical reference is
Durrett, Richard
Brownian motion and martingales in analysis.
The Wadsworth Mathematics Series. Belmont, California: Wadsworth Advanced Books & Software. A Division of Wadsworth, Inc. XI, 328 p. (1984)
The following chapters address topics you are interested in:
Boundary limits of harmonic functions. Complex Brownian motion and analytic functions.
A: The book Conformally Invariant Processes in the Plane by Lawler (American Mathematical Society, 2008) develops the theory of the Schramm-Loewner Evolution (SLE), one of the most striking applications of complex analysis to probability theory. Related material can be found on Lawler’s web page.
The book Schramm-Loewner Evolution by Kempainnen (SpringerBriefs in Mathematical Physics, 2017) covers similar topics.
The book Conformal Maps and Geometry by Beliaev (World Scientific, 2019) doesn’t seem to discuss much probability but describes itself as “an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution.” So could be worth looking at as well.
