Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium, Rosendal, Norway, August 2016

734 Pages·2018·12.11 MB·English

by  Elena Celledoni

Abel Symposia 13
Elena Celledoni
Giulia Di Nunno
Kurusch Ebrahimi-Fard
Hans Zanna Munthe-Kaas Editors
Computation and
Combinatorics
in Dynamics,
Stochastics and
Control
The Abel Symposium, Rosendal, Norway,
August 2016
ABEL SYMPOSIA
Edited by the Norwegian Mathematical Society
Moreinformationaboutthisseriesathttp://www.springer.com/series/7462
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Elena Celledoni • Giulia Di Nunno (cid:129)
Kurusch Ebrahimi-Fard (cid:129) Hans Zanna Munthe-Kaas
Editors
Computation and
Combinatorics in Dynamics,
Stochastics and Control
The Abel Symposium, Rosendal, Norway,
August 2016
123
Editors
ElenaCelledoni GiuliaDiNunno
DepartmentofMathematicalSciences DepartmentofMathematics
NorwegianUniversityofScience UniversityofOslo
andTechnology Oslo,Norway
Trondheim,Norway
KuruschEbrahimi-Fard HansZannaMunthe-Kaas
DepartmentofMathematicalSciences DepartmentofMathematics
NorwegianUniversityofScience UniversityofBergen
andTechnology Bergen,Norway
Trondheim,Norway
ISSN2193-2808 ISSN2197-8549 (electronic)
AbelSymposia
ISBN978-3-030-01592-3 ISBN978-3-030-01593-0 (eBook)
https://doi.org/10.1007/978-3-030-01593-0
LibraryofCongressControlNumber:2018966592
Mathematics Subject Classification (2010): 15A52, 16W30, 17D25, 35R60, 37E20, 60H15, 76M35,
93C10
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Foreword
TheNorwegiangovernmentestablishedtheAbelPrizeinmathematicsin2002,and
the first prize was awarded in 2003. In addition to honoring the great Norwegian
mathematicianNielsHenrikAbelbyawardinganinternationalprizeforoutstanding
scientificworkinthefieldofmathematics,theprizeshallcontributetowardraising
the status of mathematics in society and stimulate the interest for science among
schoolchildrenandstudents.Inkeepingwiththisobjective,theNielsHenrikAbel
Board has decided to finance annual Abel Symposia. The topic of the symposia
maybeselectedbroadlyintheareaofpureandappliedmathematics.Thesymposia
should be at the highest international level and serve to build bridges between
thenationalandinternationalresearchcommunities.TheNorwegianMathematical
Societyisresponsiblefortheevents.Ithasalsobeendecidedthatthecontributions
fromthese symposia shouldbe presentedin a series of proceedings,and Springer
Verlag has enthusiastically agreed to publish the series. The Niels Henrik Abel
Boardisconfidentthattheserieswillbeavaluablecontributiontothemathematical
literature.
ChairoftheNielsHenrikAbelBoard KristianRanestad
v
Preface
In recent years we have witnessed a remarkable convergence between individual
mathematical disciplines that approach deterministic and stochastic dynamical
systems from mathematical analysis, computational mathematics, and control
theoretical perspectives. One of the prime examples is the theory of rough paths,
pioneered by Terry Lyons (Oxford). Massimiliano Gubinelli (Paris/Bonn) subse-
quently developed the notions of controlled and branched rough paths. This line
of work culminated in the 2014 Fields Medal being awarded to Martin Hairer
(Warwick/London)forhisfar-reachingworkonregularitystructures,whichledhim
tobreakthroughdiscoveriesinthetheoryofstochasticpartialdifferentialequations.
Rough paths theory has strong connections to the analysis of geometric inte-
grationalgorithmsfordeterministicflows, wherethe needto understandstructure
preservation has led to the developmentof new analytical tools based on modern
algebraandcombinatorics.Recentdevelopmentsinthesefieldsprovideacommon
mathematicalframeworkforattackingmanydifferentproblemsrelatedtodifferen-
tialgeometry,analysisandalgorithmsforstochasticanddeterministicdynamics.
In the AbelSymposium2016(August16–19),leadingresearchersin the fields
of deterministic and stochastic differential equations, numerical analysis, control
theory,algebra, and random processes met at the picturesqueBarony in Rosendal
nearBergenforalivelyexchangeofresearchideasandpresentationofthecurrent
state of the art in these fields. The currentAbelSymposia volume may serve as a
pointofdepartureforexploringtheserelatedbutdiversefieldsofresearch,aswellas
anindicatorofimportantcurrentandfuturedevelopmentsinmodernmathematics.
Trondheim,Norway ElenaCelledoni
Oslo,Norway GiuliaDiNunno
Trondheim,Norway KuruschEbrahimi-Fard
Bergen,Norway HansZannaMunthe-Kaas
vii
Contents
FacilitatedExclusionProcess................................................... 1
JinhoBaik,GuillaumeBarraquand,IvanCorwin,andTouficSuidan
Stochastic FunctionalDifferentialEquations and Sensitivity
toTheirInitialPath.............................................................. 37
D.R.Baños,G.DiNunno,H.H.Haferkorn,andF.Proske
Grassmannian Flows and Applications to Nonlinear Partial
DifferentialEquations........................................................... 71
MargaretBeck,AnastasiaDoikou,SimonJ.A.Malham,
andIoannisStylianidis
GogandMagogTriangles....................................................... 99
PhilippeBiane
TheClebschRepresentationinOptimalControlandLowRank
IntegrableSystems............................................................... 129
AnthonyM.Bloch,FrançoisGay-Balmaz,andTudorS.Ratiu
TheGeometryofCharactersofHopfAlgebras .............................. 159
GeirBogfjellmoandAlexanderSchmeding
ShapeAnalysisonHomogeneousSpaces:A GeneralisedSRVT
Framework........................................................................ 187
ElenaCelledoni,SølveEidnes,andAlexanderSchmeding
UniversalityinNumericalComputationwithRandomData:Case
Studies,AnalyticalResultsandSomeSpeculations.......................... 221
PercyDeiftandThomasTrogdon
BSDEswithDefaultJump ...................................................... 233
RoxanaDumitrescu,MiryanaGrigorova,Marie-ClaireQuenez,
andAgnèsSulem
ix
x Contents
The Faà di Bruno Hopf Algebra for Multivariable Feedback
RecursionsintheCenterProblemforHigherOrderAbelEquations ..... 265
KuruschEbrahimi-FardandW.StevenGray
Continuous-Time Autoregressive Moving-AverageProcesses
inHilbertSpace .................................................................. 297
FredEspenBenthandAndréSüss
Pre-andPost-LieAlgebras:TheAlgebro-GeometricView................. 321
GunnarFløystadandHansMunthe-Kaas
ExtensionoftheProductofaPost-LieAlgebraandApplication
totheSISOFeedbackTransformationGroup................................ 369
LoïcFoissy
InfiniteDimensionalRoughDynamics ........................................ 401
MassimilianoGubinelli
HeavyTailedRandomMatrices:HowTheyDifferfromtheGOE,
andOpenProblems.............................................................. 415
AliceGuionnet
AnAnalyst’sTakeontheBPHZTheorem .................................... 429
MartinHairer
ParabolicAndersonModelwithRoughDependenceinSpace.............. 477
YaozhongHu,JingyuHuang,KhoaLê,DavidNualart,andSamyTindel
PerturbationofConservationLawsandAveragingonManifolds.......... 499
Xue-MeiLi
Free Probability, Random Matrices, and Representations
ofNon-commutativeRationalFunctions...................................... 551
TobiasMaiandRolandSpeicher
AReviewonComodule-Bialgebras............................................ 579
DominiqueManchon
Renormalization:AQuasi-shuffleApproach ................................. 599
FrédéricMenousandFrédéricPatras
Hopf Algebra Techniques to Handle Dynamical Systems
andNumericalIntegrators...................................................... 629
AnderMuruaandJesúsM.Sanz-Serna
QuantitativeLimitTheoremsforLocalFunctionalsofArithmetic
RandomWaves................................................................... 659
GiovanniPeccatiandMauriziaRossi
Contents xi
CombinatoricsonWordsandtheTheoryofMarkoff ....................... 691
ChristopheReutenauer
AnAlgebraicApproachtoIntegrationofGeometricRoughPaths ........ 709
DanyuYang