Self-Duality of Markov Processes and Intertwining Functions
Tóm tắt
Từ khóa
Tài liệu tham khảo
Andrews, G.E., Askey, R., Roy, R.: Special Functions. Encycl. Math. Appl. 71 Cambridge University Press (1999)
Belitsky, V., Schütz, G.M.: Self-duality for the two-component asymmetric simple exclusion process. J. Math. Phys. 56(8), 083302 (2015)
Belitsky, V., Schütz, G.M.: Quantum algebra symmetry of the ASEP with second-class particles. J. Stat. Phys. 161(5), 821–842 (2015)
Belitsky, V., Schütz, G.M.: Self-duality and shock dynamics in the n-species priority ASEP. Stochastic Processes and their Applications 128(4), 1165–1207 (2017)
Bernardin, C.: Superdiffusivity of asymmetric energy model in dimensions 1 and 2. J. Math. Phys. 49(10), 103301 (2008)
Borodin, A., Corwin, I., Gorin, V.: Stochastic six-vertex model. Duke Math. J. 165(3), 563–624 (2016)
Borodin, A., Corwin, I., Sasamoto, T.: From duality to determinants for q-TASEP and ASEP. Ann. Probab. 42(6), 2314–2382 (2014)
Carinci, G., Giardinà, C., Giberti, C., Redig, F.: Duality for stochastic models of transport. J. Stat. Phys. 152(4), 657–697 (2013)
Carinci, G., Giardin, C., Redig, F., Sasamoto, T.: A generalized asymmetric exclusion process with U q ( s l 2 ) $U_q(\mathfrak {sl}_2)$ stochastic duality. Probab. Theory Relat. Fields 166, 887–933 (2016)
Carinci, G., Giardinà, C., Redig, F., Sasamoto, T.: Asymmetric Stochastic Transport Models with U q ( s u ( 1 , 1 ) ) ${\mathscr{U}}_q (\mathfrak {su}(1, 1))$ Symmetry. J. Stat. Phys. 163(2), 239–279 (2016)
Carinci, G., Giardinà, C., Giberti, C., Redig, F.: Dualities in population genetics: a fresh look with new dualities. Stochastic Processes and their Applications 125(3), 941–969 (2015)
Chen, Z., de Gier, J., Wheeler, M.: Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation. Preprint arXiv: 1709.06227 . International Mathematics Research Notices, rny159 (2017)
Corwin, I., Petrov, L.: Stochastic higher spin vertex models on the line. Commun. Math. Phys. 343(2), 651–700 (2016)
Corwin, I., Shen, H., Tsai, L.-C.: ASEP(q, j) converges to the KPZ equation (2016)
De Masi, A., Presutti, E.: Mathematical methods for hydrodynamic limits. Springer (2006)
Franceschini, C., Giardinà, C.: Stochastic Duality and Orthogonal Polynomials. arXiv: 1701.09115 (2017)
Giardinà, C., Kurchan, J.: The Fourier law in a momentum-conserving chain. J. Stat. Mech: Theory Exp. 05(2005), P05009 (2005)
Giardinà, C., Kurchan, J., Redig, F.: Duality and exact correlations for a model of heat conduction. J. Math. Phys. 48(3), 033301 (2007)
Giardinà, C., Kurchan, J., Redig, F., Vafayi, K.: Duality and hidden symmetries in interacting particle systems. J. Stat. Phys. 135(1), 25–55 (2009)
Giardinà, C., Redig, F., Vafayi, K.: Correlation inequalities for interacting particle systems with duality. J. Stat. Phys. 141(2), 242–263 (2010)
Groenevelt, W.: Orthogonal stochastic duality functions from Lie algebra representations. arXiv: 1709.05997 (2017)
Jansen, S., Kurt, N.: On the notion(s) of duality for Markov processes. Probab. Surv. 11, 59–120 (2014)
Keisling, J.D.: An ergodic theorem for the symmetric generalized exclusion process. Markov Process. Relat. Fields 4, 351–379 (1998)
Kipnis, C., Marchioro, C., Presutti, E.: Heat flow in an exactly solvable model. J. Stat. Phys. 27(1), 65–74 (1982)
Koekoek, R., Lesky, P.A., Swarttouw, R.F.: Hypergeometric Orthogonal Polynomials and their q-Analogues. Springer (2010)
Koelink, H.T., Van der Jeugt, J.: Convolution for orthogonal polynomials from Lie and quantum algebra representations. SIAM J. Math. Annal. 29, 794–822 (1998)
Kuan, J.: Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two. J. Phys. A Math. Theor. 49(11), 115002 (2016)
Kuan, J.: A Multi-species ASEP(q, j) and q-TAZRP with stochastic duality. arXiv: 1605.00691 (2016)
Kuan, J.: An algebraic construction of duality functions for the stochastic U q ( A n ( 1 ) ) $ {U_q} (A_n^{(1)})$ vertex model and its degenerations. arXiv: 1701.04468 (2017)
Mangazeev, V.: On the Yang–Baxter equation for the six-vertex model. Nucl. Phys. B 882, 70–96 (2014)
Möhle, M.: The concept of duality and applications to Markov processes arising in neutral population genetics models. Bernoulli 5(5), 761–777 (1999)
Redig, F., Sau, F.: Duality functions and stationary product measures. arXiv: 1702.07237 (2017)
Sasamoto, T., Spohn, H.: One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality. Phys. Rev. Lett. 104(23), 230602 (2010)
Schütz, G.M.: Duality relations for asymmetric exclusion processes. J. Stat. Phys. 86(5), 1265–1287 (1997)
Schütz, G.M., Sandow, S.: Non-Abelian symmetries of stochastic processes: Derivation of correlation functions for random-vertex models and disordered-interacting-particle systems. Phys. Rev. E 49(4), 2726 (1994)