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On the power series representation of smooth conformal martingales

Nguyen Xuan-loc
1986 Nagoya mathematical journal  
An a-priori estimate in the L2-norm of the above mentioned remainder term is given and consequently a power series representation of smooth conformal martingales is obtained (Theorem 4).  ...  We introduce here the notion of (stochastically) differentiable process with respect to a fixed conformal martingale and compute the remainder term of the Taylor expansion of the given process (Definition  ...  The author would like to thank the referee for pointing to him an error in the proof of Proposition 3 and for giving him many interesting comments.  ... 
doi:10.1017/s0027763000000556 fatcat:nmxbbcvorbecnikrz3nnr7gqk4

Page 185 of Mathematical Reviews Vol. 50, Issue 1 [page]

1975 Mathematical Reviews  
From the preface: “This conference was planned with the inten- tion of discussing the question: Martingales having proved to be a powerful tool, can they now be the subject of a probabilistic theory?  ...  The second-order moments and correla- tion functions. 10. Equations with a random telegraph coefficient. 11. Application of a limit theorem. 12. Perturbation results for coupled lines.  ... 

Plug-in martingales for testing exchangeability on-line [article]

Valentina Fedorova, Alex Gammerman, Ilia Nouretdinov, Vladimir Vovk
2012 arXiv   pre-print
We extend known techniques for constructing exchangeability martingales and show that our new method is competitive with the martingales introduced before.  ...  This paper is devoted to testing the assumption of exchangeability on-line: the examples arrive one by one, and after receiving each example we would like to have a valid measure of the degree to which  ...  Acknowledgments We are indebted to Royal Holloway, University of London, for continued support and funding.  ... 
arXiv:1204.3251v2 fatcat:s4mqe7klqrefdfbzjfsw3cliuu

Testing randomness [article]

Vladimir Vovk
2020 arXiv   pre-print
Validity results limit the probability of a false alarm or the frequency of false alarms for various procedures based on conformal martingales, including conformal versions of the CUSUM and Shiryaev-Roberts  ...  Efficiency results establish connections between randomness, exchangeability, and conformal martingales.  ...  Acknowledgements The original version of this paper was written in support of my poster at ISIPTA 2019 (Eleventh International Symposium on Imprecise Probabilities: Theories and Applications) presented  ... 
arXiv:1906.09256v3 fatcat:o6dvnxsu45dm5ohgj7tgcgfznm

Conformal Field Theory, Vertex Operator Algebra and Stochastic Loewner Evolution in Ising Model [article]

Ali Zahabi
2015 arXiv   pre-print
We review the algebraic and analytic aspects of the conformal field theory (CFT) and its relation to the stochastic Loewner evolution (SLE) in an example of the Ising model.  ...  These constructions lead to the conformal field theory of the Fock space fields and the fermionic Fock space of states and their relations in case of the Ising free fermions.  ...  Acknowledgements: I would like to thank Kalle Kytölä for useful and interesting discussions and comments. This work was supported by the Academy of Finland.  ... 
arXiv:1505.01405v1 fatcat:m6duwzkisjgu3me5dr72yw22k4

Logarithmic conformal null vectors and SLE

S. Moghimi-Araghi, M.A. Rajabpour, S. Rouhani
2004 Physics Letters B  
In this letter we introduce an extension of Loewner evolution, which consists of two coupled equations and connect the martingales of these equations to the null vectors of logarithmic conformal field  ...  Formal Loewner evolution is connected to conformal field theory.  ...  Saadat and M. R. Rahimi-Tabar for their helpful discussions.  ... 
doi:10.1016/j.physletb.2004.09.016 fatcat:hpeq6mqxz5hgfddpcupf7cwe3m

Page 2021 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
Engl (Linz) 88d:60172 60H99 60G44 Nguyen Xuan Loc (VN-ICC) On the power series representation of smooth conformal martingales. . Nagoya Math. J. 103 (1986), 15-27. Let W be a conformal martingale.  ...  in W: M(t)=M(0)+)> + M(0)((2) - W(0))". n=1 The author applies this to power series expansions of finely holomorphic functions and to isolated singularities of conformal martingales.  ... 

Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales

Michel Bauer, Denis Bernard, Kalle Kytölä
2005 Journal of statistical physics  
We give examples of such multiple SLEs and discuss how a choice of conformal block is related to geometric configuration of the interfaces and what is the physical meaning of mixed conformal blocks.  ...  A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality  ...  At the critical temperature and in the continuum limit, the system is believed to be conformally invariant and physicists have developed many powerful techniques, known under the name conformal field theory  ... 
doi:10.1007/s10955-005-7002-5 fatcat:e7xwcxzyd5dovos3msztoogkni

Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation

Matteo Casserini, Freddy Delbaen
2012 Electronic Journal of Probability  
In this article, we study predictable projections of stochastic integrals with respect to the conformal Brownian motion, extending the connection between powers of the conformal Brownian motion and the  ...  Finally, our results are applied to Widder's representation for a class of Brownian martingales, retrieving a characterization for the moments of Widder's measure.  ...  Conformal martingales have been introduced by Getoor and Sharpe [4] to prove the duality between the Hardy space H 1 and the space BM O in the martingale setting: conformal martingales later played an  ... 
doi:10.1214/ejp.v17-1883 fatcat:om63jmkwn5hwpm27vtavphyjsu

Page 270 of Mathematical Reviews Vol. , Issue 83a [page]

1983 Mathematical Reviews  
Using generating functions and Lagrange’s theorem for the expansion of a power series explicit expressions are deduced for the probabilities of the player’s capital at the nth step.”  ...  Schwartz [ Semimartingales on manifolds, and conformal martingales on complex analytic manifolds, Lecture Notes in Math., 780, Springer, Berlin, 1980; MR 82m:60051] has defined semimartingales in random  ... 

UST branches, martingales, and multiple SLE(2) [article]

Alex Karrila
2020 arXiv   pre-print
The obtained weighting transforms of the discrete martingales and the limiting SLE processes, respectively, only rely on a discrete domain Markov property and (essentially) the convergence of partition  ...  By recent results, this also characterizes the "global" scaling limit of the full collection of full curves.  ...  Indeed, the description of the scaling limit is given merely in terms of H and X , not their conformal (pre)images, the actual limiting domain Λ and prime ends p 1 , . . . , p 2N .  ... 
arXiv:2002.07103v2 fatcat:6t7c3i7jsnhvpawstb2a6s5w4i

LERW as an Example of Off-Critical SLEs

Michel Bauer, Denis Bernard, Kalle Kytölä
2008 Journal of statistical physics  
Such a description is bound to be quite complicated because outside the critical point one has a finite correlation length and therefore no conformal invariance.  ...  On the other hand, we show that it is possible to understand the Loewner driving function of the continuum limit of off-critical LERWs, thus providing an example of application of SLE-like techniques to  ...  formal expansion in powers of ε.  ... 
doi:10.1007/s10955-008-9569-0 fatcat:qeaf5qwvdnhz7op27ttuxmjsea

Page 5072 of Mathematical Reviews Vol. , Issue 83m [page]

1983 Mathematical Reviews  
By means of its Doob-Meyer decomposition we construct a martingale and show that this martingale converges weakly to the Wiener process.  ...  The authors regard their parameter p» as a location parameter and propose to use the relation > as a measure of conformity to H,.  ... 

Schramm-Loewner Evolution [article]

Gregory F. Lawler
2007 arXiv   pre-print
This seems more natural from the perspective of limits of lattice systems and seems to be more useful when extending SLE to non-simply connected domains.  ...  (However, I do not discuss non-simply connected domains in these notes.) o I have made more use of the Girsanov theorem in studying corresponding martingales and local martingales.  ...  .) • I have made more use of the Girsanov theorem in studying corresponding martingales and local martingales.  ... 
arXiv:0712.3256v1 fatcat:q37chblcerf2fpfbh6v2kwnkvu

Martingales of stochastic Laplacian growth [article]

Oleg Alekseev
2019 arXiv   pre-print
A family of exponential martingales of a stochastic Laplacian growth problem is proposed.  ...  conformal field theory in the Coulomb gas framework.  ...  LG stands out against the other nonlocal growth processes, because of its powerful properties, unusual for most nonlinear growth processes, such as infinitely many conservation laws [Ric72] and closed  ... 
arXiv:1912.01370v1 fatcat:gc7wxwbssvab5ejpeegges677m
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