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Trans. Am. Math. Soc. 361, 1963–1999 (2009)\nBass, R.F., Kassmann, M., Kumagai, T.: Symmetric jump processes: localization, heat kernels, and convergence. Ann. Inst. Henri Poincaré (2009, in press)\nBass R.F., Kumagai T.: Symmetric Markov chains on \\({\\mathbb{Z}^d}\\) with unbounded range. Trans. Am. Math. Soc. 360, 2041–2075 (2008)\nCarlen E.A., Kusuoka S., Stroock D.W.: Upper bounds for symmetric Markov transition functions. Ann. Inst. Henri Poincaré-Probab. Stat. 23, 245–287 (1987)\nChen Z.-Q., Kumagai T.: Heat kernel estimates for stable-like processes on d-sets. Stoch. Process Appl. 108, 27–62 (2003)\nChen Z.-Q., Kumagai T.: Heat kernel estimates for jump processes of mixed type on metric measure spaces. Probab. Theory Relat. Fields 140, 277–317 (2008)\nChen, Z.-Q., Kumagai, T.: A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps. Rev. Mat. Iberoam. (2009, in press)\nDe Masi A., Ferrari P.A., Goldstein S., Wick W.D.: An invariance principle for reversible Markov processes. Applications to random motions in random environments. J. Stat. Phys. 55, 787–855 (1989)\nFoondun, M.: Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part. Preprint (2006)\nFukushima M., Oshima Y., Takeda M.: Dirichlet Forms and Symmetric Markov Processes. deGruyter, Berlin (1994)\nHusseini R., Kassmann M.: Markov chain approximations for symmetric jump processes. Potential Anal. 27, 353–380 (2007)\nStroock D.W., Varadhan S.R.S.: Multidimensional Diffusion Processes. Springer, Berlin (1979)\nStroock D.W., Zheng W.: Markov chain approximations to symmetric diffusions. Ann. Inst. Henri. Poincaré-Probab. Statist. 33, 619–649 (1997)",{"EN":378,"VI":379},"For each n let \n                \n                  \n                \n                $${Y^{(n)}_t}$$\n               be a continuous time symmetric Markov chain with state space \n                \n                  \n                \n                $${n^{-1} \\mathbb{Z}^d}$$\n               . Conditions in terms of the conductances are given for the convergence of the \n                \n                  \n                \n                $${Y^{(n)}_t}$$\n               to a symmetric Markov process Y\n                        \n                  t\n                 on \n                \n                  \n                \n                $${\\mathbb{R}^d}$$\n               . We have weak convergence of \n                \n                  \n                \n                $$\\{{Y^{(n)}_t: t \\leq t_0\\}}$$\n               for every t\n                        0 and every starting point. The limit process Y has a continuous part and may also have jumps.","Với mỗi n, ký hiệu \n                \n                  \n                \n                $${Y^{(n)}_t}$$\n               là một chuỗi Markov đối xứng liên tục theo thời gian với không gian trạng thái \n                \n                  \n                \n                $${n^{-1} \\mathbb{Z}^d}$$\n               . Các điều kiện liên quan đến tính dẫn điện được đưa ra để đảm bảo sự hội tụ của \n                \n                  \n                \n                $${Y^{(n)}_t}$$\n               về một quá trình Markov đối xứng Y\n                        \n                  t\n                 trên \n                \n                  \n                \n                $${\\mathbb{R}^d}$$\n               . 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CRAS, Paris Série I, Math. 319, 397–400 (1994)\nAnderson, R.D., Klee, V.L.Jr.: Convex functions and upper semicontinuous collections. Duke Math. J. 19, 349–357 (1952)\nAppell, P.: Mémoire sur déblais et les remblais des systèmes continus ou discontinus. Mémoires présentées par divers savants à l’Académie des Sciences de l’Institut de France. Paris, I. N. 29, 1–208 (1887)\nAppell, P.: Le problème géométrique des déblais et des remblais. Mémorial des Sciences Mathématiques, fasc. XXVII, Paris, (1928)\nBickel, P.J., Freedman, D.A.: Some asymptotic theory for the bootstrap. Ann. Statis. 9(6), 1196–1217 (1981)\nBrenier, Y.: Polar factorization and monotone rearrangement of vector valued functions. Comm. pure Appl. Math. 44, 375-417 (1991)\nCaffarelli, L.A.: The regularity of mappings with a convex potential. J. Am. Math. Soc. 5, 99–104 (1992)\nDacarogna, B., Moser, J.: On a partial differential equation involving the Jacobian determinant. Ann. Inst. Henri Poincaré, Analyse non-linéaire. 7, 1–26 (1990)\nDellacherie, C., Meyer, P.A.: Probabilités et Potentiel, Ch. I à IV. Paris, Hermann, 1975\nDjellout, H., Guillin, A., Wu, L.: Transportation cost-information inequalities for random dynamical systems and diffusions. Preprint, December 2002\nDunford, N., Schwartz, J.T.: Linear Operators. 2, Interscience, 1963\nFernique, X.: Extension du théorème de Cameron-Martin aux translations aléatoires. Comptes Rendus Mathématiques 335(1), 65–68 (2002)\nFernique, X.: Comparaison aux mesures gaussiennes, espaces autoreproduisants. Une application des propriétés isopérimétriques. Preprint\nFeyel, D., de La Pradelle, A.: Capacités gaussiennes. Annales de l’Institut Fourier t.41, f.1, 49–76 (1991)\nFeyel, D., Üstünel, A.S.: The notion of convexity and concavity on Wiener space. J. Funct. Anal. 176, 400–428 (2000)\nFeyel, D., Üstünel, A.S.: Transport of measures on Wiener space and the Girsanov theorem. Comptes Rendus Mathématiques. 334(1), 1025–1028 (2002)\nGangbo, W., McCann, R.J.: The geometry of optimal transportation. Acta Mathematica 177, 113–161 (1996)\nIto, K., Nisio, M.: On the convergence of sums of independent Banach space valued random variables. Osaka J. Math. 5, 35–48 (1968)\nKantorovitch, L.V.: On the transfer of masses. Dokl. Acad. Nauk. SSSR 37, 227–229 (1942)\nMarton, K.: Bounding -distance by informational divergence: a method to prove measure concentration. Ann. Probab. 24(2), 857–866 (1996)\nMcCann, R.J.: Existence and uniqueness of monotone measure-preserving maps. Duke Math. J. 80, 309–323 (1995)\nMcCann, R.J.: A convexity principle for interacting gases. Adv. Math. 128, 153–179 (1997)\nMonge, G.: Mémoire sur la théorie des déblais et des remblais. Histoire de l’Académie Royale des Sciences, Paris, 1781\nRachev, S.T.; The Monge-Kantorovitch transference problem. Th. prob. Appl. 49, 647–676 (1985)\nRockafellar, T.: Convex Analysis. Princeton University Press, Princeton, 1972\nSudakov, V.N.: Geometric problems in the theory of infinite dimensional probability distributions. Proc. Steklov Inst. Math. 141, 1–178 (1979)\nTalagrand, M.: Transportation cost for Gaussian and other product measures. Geom. Funct. Anal. 6, 587–600 (1996)\nThomas, E.: The Lebesgue-Nikodym theorem for vector valued Radon measures. Memoirs of A.M.S. 139, (1974)\nÜstünel, A.S.: Representation of distributions on Wiener space and Stochastic Calculus of Variations. J. Funct. Anal. 70, 126–139 (1987)\nÜstünel, A.S.: Introduction to Analysis on Wiener Space. Lecture Notes in Math. 1610, Springer, 1995\nÜstünel, A.S., Zakai, M.: Transformation of Measure on Wiener Space. Springer Monographs in Mathematics. Springer Verlag, 1999",{"EN":687},"Let (W,μ,H) be an abstract Wiener space assume two ν\n                  i\n                ,i=1,2 probabilities on (W,ℬ(W)). We give some conditions for the Wasserstein distance between ν1 and ν2 with respect to the Cameron-Martin space \n                \n               to be finite, where the infimum is taken on the set of probability measures β on W×W whose first and second marginals are ν1 and ν2. In this case we prove the existence of a unique (cyclically monotone) map T=I\n                        \n                  W\n                +ξ, with ξ:W→H, such that T maps ν1 to ν2. Moreover, if ν2≪μ, then T is stochastically invertible, i.e., there exists S:W→W such that S○T=I\n                        \n                  W\n                 ν1 a.s. and T○S=I\n                        \n                  W\n                 ν2 a.s. If, in addition, ν1=μ, then there exists a 1-convex function φ in the Gaussian Sobolev space \n                \n               such that ξ=∇φ. These results imply that the quasi-invariant transformations of the Wiener space with finite Wasserstein distance from μ can be written as the composition of a transport map T and a rotation, i.e., a measure preserving map. We give also 1-convex sub-solutions and Ito-type solutions of the Monge-Ampère equation on W.\n",{"EN":689},"Monge-Kantorovitch Measure Transportation and Monge-Ampère Equation on Wiener Space",{"VOID":691},"10.1007\u002Fs00440-003-0307-x","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00440-003-0307-x",[694,709],{"id":695,"sortIndex":411,"researcher":20,"roles":696,"affiliations":697,"properties":706},"ac4c0394-72a2-4d6f-8953-d90d2d2405fb",[317],[698],{"id":20,"sortIndex":21,"affiliation":699,"properties":20},{"id":700,"createTime":701,"updateTime":701,"relativeEntities":702,"slug":20,"properties":703,"entityType":57,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"3d7e91bb-414f-42e1-8f60-d09a45adfde4","2024-02-08T00:37:55.795+00:00",[],{"title":704},{"VI":705},"ENST, Dépt., Infres, Paris Cedex 13, France",{"title":707},{"VI":708},"A. S. 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(2014). arXiv:1408.0632",{},{"id":20,"text":924,"url":20,"identifiers":925},"Osada, H., Tanemura, H.: Strong Markov property of determinantal processes with extended kernels. (2014). arXiv:1412.8678",{},{"id":20,"text":927,"url":20,"identifiers":928},"Spohn, H.: Interacting Brownian particles: a study of Dyson’s model. In: Hydrodynamic behavior and interacting particle systems, pp. 151-179. Springer (1987)",{"doi":929},"10.1007\u002F978-1-4684-6347-7_13",{"id":20,"text":931,"url":20,"identifiers":932},"Valkó, B., Virág, B.: Continuum limits of random matrices and the Brownian carousel. Invent. 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Probab.; citation_title=Some examples of dynamics for Gelfand-Tsetlin patterns; citation_author=J Warren, P Windridge; citation_volume=14; citation_issue=59; citation_publication_date=2009; citation_pages=1745-1769; citation_id=CR38",{"EN":944},"The explicit biorthogonalization method, developed in [24] for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evolution of several interacting particle systems in the KPZ universality class. The method is applied to sequential and parallel update versions of each of the four variants of discrete time TASEP (with Bernoulli and geometric jumps, and with block and push dynamics) which have determinantal transition probabilities; to continuous time PushASEP; and to a version of TASEP with generalized update. In all cases, multipoint distribution functions are expressed in terms of a Fredholm determinant with an explicit kernel involving hitting times of certain random walks to a curve defined by the initial data of the system. The method is further applied to systems of interacting caterpillars, an extension of the discrete time TASEP models which generalizes sequential and parallel updates.",{"EN":946},"TASEP and generalizations: method for exact solution",{"VOID":948},"10.1007\u002Fs00440-022-01129-w","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00440-022-01129-w","https:\u002F\u002Flink.springer.com\u002Fcontent\u002Fpdf\u002F10.1007\u002Fs00440-022-01129-w.pdf",[952,967],{"id":953,"sortIndex":411,"researcher":20,"roles":954,"affiliations":955,"properties":964},"3f7a6cc4-cb5c-40d6-a68e-99b48c588a06",[317],[956],{"id":20,"sortIndex":21,"affiliation":957,"properties":20},{"id":958,"createTime":959,"updateTime":959,"relativeEntities":960,"slug":20,"properties":961,"entityType":57,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"7b13f2d2-8888-4fb7-bda0-0abe8196947c","2023-12-13T00:55:12.616+00:00",[],{"title":962},{"VI":963},"Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI-CNRS 2807), Universidad de Chile, Piso 5, Chile",{"title":965},{"VI":966},"Remenik, 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