02906nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002400133040001400157072001500171072001700186084002900203100002900232245015600261260008200417300003400499336002600533337002600559338003600585347002400621490006100645506006600706520147100772650002402243650002402267650005302291650004002344650002402384856003502408856007702443271-220422CH-001817-320220422114427.0a fot ||| 0|cr nn mmmmamaa220422e20220419sz fot ||| 0|eng d a978398547514870a10.4171/ELM/342doi ach0018173 7aPB2bicssc 7aPBWL2bicssc a60-xxa35-xxa81-xx2msc1 aBerglund, Nils,eauthor.10aAn Introduction to Singular Stochastic PDEsh[electronic resource] :bAllenâ€“Cahn Equations, Metastability, and Regularity Structures /cNils Berglund3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2022 a1 online resource (230 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aStochastic partial differential equations (SPDEs) model the evolution in time of spatially
extended systems subject to a random driving. Recent years have witnessed tremendous progress in the
theory of so-called singular SPDEs. These equations feature a singular, distribution-valued driving term, a
typical example being spacetime white noise, which makes them ill-posed as such. In many cases, it is
however possible to make sense of these equations by applying a so-called renormalisation procedure,
initially introduced in quantum field theory.
This book gives a largely self-contained exposition of the subject of regular and singular SPDEs in the
particular case of the Allenâ€“Cahn equation, which models phase separation. Properties of the equation are
discussed successively in one, two and three spatial dimensions, allowing to introduce new difficulties of the
theory in an incremental way. In addition to existence and uniqueness of solutions, aspects of long-time
dynamics such as invariant measures and metastability are discussed. A large part of the last chapter, about
the three-dimensional case, is dedicated to the theory of regularity structures, which has been developed by
Martin Hairer and co-authors in the last years, and allows to describe a large class of singular SPDEs.
The book is intended for graduate students and researchers in mathematics and physics with prior knowledge in stochastic processes or stochastic calculus.07aMathematics2bicssc07aStochastics2bicssc07aProbability theory and stochastic processes2msc07aPartial differential equations2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/ELM/34423cover imageuhttps://www.ems-ph.org/img/books/9783985470143_Berglund.jpg