Petrov, Leonid; Saenz, Axel Mapping TASEP Back in time. (English) Zbl 1490.60281 Probab. Theory Relat. Fields 182, No. 1-2, 481-530 (2022). MSC: 60K35 05E05 60J60 82C22 82B23 PDF BibTeX XML Cite \textit{L. Petrov} and \textit{A. Saenz}, Probab. Theory Relat. Fields 182, No. 1--2, 481--530 (2022; Zbl 1490.60281) Full Text: DOI arXiv OpenURL
Petrov, Leonid Parameter permutation symmetry in particle systems and random polymers. (English) Zbl 1467.82059 SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 021, 34 p. (2021). MSC: 82C22 82C23 82D60 60C05 60J27 PDF BibTeX XML Cite \textit{L. Petrov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 021, 34 p. (2021; Zbl 1467.82059) Full Text: DOI arXiv OpenURL
Liechty, Karl; Wang, Dong Asymptotics of free fermions in a quadratic well at finite temperature and the Moshe-Neuberger-Shapiro random matrix model. (English. French summary) Zbl 1447.82014 Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 2, 1072-1098 (2020). Reviewer: Hasan Akin (Gaziantep) MSC: 82B26 15B52 60G55 PDF BibTeX XML Cite \textit{K. Liechty} and \textit{D. Wang}, Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 2, 1072--1098 (2020; Zbl 1447.82014) Full Text: DOI arXiv Euclid OpenURL
Imamura, T.; Sasamoto, T. The \(q\)-TASEP with a random initial condition. (English. Russian original) Zbl 1418.82007 Theor. Math. Phys. 198, No. 1, 69-88 (2019); translation from Teor. Mat. Fiz. 198, No. 1, 79-100 (2019). MSC: 82C41 60K35 60B20 33C15 81R50 PDF BibTeX XML Cite \textit{T. Imamura} and \textit{T. Sasamoto}, Theor. Math. Phys. 198, No. 1, 69--88 (2019; Zbl 1418.82007); translation from Teor. Mat. Fiz. 198, No. 1, 79--100 (2019) Full Text: DOI arXiv OpenURL
Lee, Eunghyun; Wang, Dong Distributions of a particle’s position and their asymptotics in the \(q\)-deformed totally asymmetric zero range process with site dependent jumping rates. (English) Zbl 1422.60159 Stochastic Processes Appl. 129, No. 5, 1795-1828 (2019). MSC: 60K35 82C22 PDF BibTeX XML Cite \textit{E. Lee} and \textit{D. Wang}, Stochastic Processes Appl. 129, No. 5, 1795--1828 (2019; Zbl 1422.60159) Full Text: DOI arXiv OpenURL
Imamura, Takashi; Sasamoto, Tomohiro Fluctuations for stationary \(q\)-TASEP. (English) Zbl 1416.82030 Probab. Theory Relat. Fields 174, No. 1-2, 647-730 (2019). MSC: 82C22 60K35 33D52 44A12 PDF BibTeX XML Cite \textit{T. Imamura} and \textit{T. Sasamoto}, Probab. Theory Relat. Fields 174, No. 1--2, 647--730 (2019; Zbl 1416.82030) Full Text: DOI arXiv OpenURL
Kuan, Jeffrey Probability distributions of multi-species \(q\)-TAZRP and ASEP as double cosets of parabolic subgroups. (English) Zbl 1407.05248 Ann. Henri Poincaré 20, No. 4, 1149-1173 (2019). MSC: 05E15 60K35 20F55 PDF BibTeX XML Cite \textit{J. Kuan}, Ann. Henri Poincaré 20, No. 4, 1149--1173 (2019; Zbl 1407.05248) Full Text: DOI arXiv OpenURL
Babelon, O.; Kozlowski, K. K.; Pasquier, V. The Toda\(_2\) chain. (English) Zbl 1411.81107 Lett. Math. Phys. 109, No. 2, 225-241 (2019). MSC: 81R10 81T40 81R12 82B20 37K10 PDF BibTeX XML Cite \textit{O. Babelon} et al., Lett. Math. Phys. 109, No. 2, 225--241 (2019; Zbl 1411.81107) Full Text: DOI arXiv OpenURL
Corwin, Ivan Exactly solving the KPZ equation. (English) Zbl 1423.60153 Damron, Michael (ed.) et al., Random growth models. AMS short course “Random Growth Models”, Atlanta, GA, USA, January 2–3, 2017. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Appl. Math. 75, 203-254 (2018). MSC: 60K35 60K37 82B43 PDF BibTeX XML Cite \textit{I. Corwin}, Proc. Symp. Appl. Math. 75, 203--254 (2018; Zbl 1423.60153) Full Text: DOI arXiv OpenURL
Takeyama, Yoshihiro On the eigenfunctions for the multi-species \(q\)-boson system. (English) Zbl 1446.17042 Funkc. Ekvacioj, Ser. Int. 61, No. 3, 349-376 (2018). MSC: 17B80 81R12 60K35 33C52 PDF BibTeX XML Cite \textit{Y. Takeyama}, Funkc. Ekvacioj, Ser. Int. 61, No. 3, 349--376 (2018; Zbl 1446.17042) Full Text: DOI arXiv OpenURL
Aggarwal, Amol Dynamical stochastic higher spin vertex models. (English) Zbl 1401.82011 Sel. Math., New Ser. 24, No. 3, 2659-2735 (2018). Reviewer: Nasir N. Ganikhodjaev (Kuantan) MSC: 82B23 60K35 81R50 PDF BibTeX XML Cite \textit{A. Aggarwal}, Sel. Math., New Ser. 24, No. 3, 2659--2735 (2018; Zbl 1401.82011) Full Text: DOI arXiv OpenURL
van Diejen, Jan Felipe; Emsiz, Erdal; Zurrián, Ignacio Nahuel Completeness of the Bethe ansatz for an open \(q\)-Boson system with integrable boundary interactions. (English) Zbl 1388.81240 Ann. Henri Poincaré 19, No. 5, 1349-1384 (2018). MSC: 81S22 81T25 82B23 81V70 33D80 42B25 PDF BibTeX XML Cite \textit{J. F. van Diejen} et al., Ann. Henri Poincaré 19, No. 5, 1349--1384 (2018; Zbl 1388.81240) Full Text: DOI arXiv OpenURL
Kuan, Jeffrey An algebraic construction of duality functions for the stochastic \(\mathcal U_q(A_n^{(1)})\) vertex model and its degenerations. (English) Zbl 1394.82004 Commun. Math. Phys. 359, No. 1, 121-187 (2018). Reviewer: Nasir N. Ganikhodjaev (Kuantan) MSC: 82B20 82C22 81R50 PDF BibTeX XML Cite \textit{J. Kuan}, Commun. Math. Phys. 359, No. 1, 121--187 (2018; Zbl 1394.82004) Full Text: DOI arXiv OpenURL
Borodin, Alexei; Petrov, Leonid Higher spin six vertex model and symmetric rational functions. (English) Zbl 1405.60141 Sel. Math., New Ser. 24, No. 2, 751-874 (2018). Reviewer: Boris Granovsky (Haifa) MSC: 60K35 05E05 82B23 PDF BibTeX XML Cite \textit{A. Borodin} and \textit{L. Petrov}, Sel. Math., New Ser. 24, No. 2, 751--874 (2018; Zbl 1405.60141) Full Text: DOI arXiv OpenURL
Kuniba, A.; Mangazeev, V. V. Density and current profiles in \(\operatorname{U}_q(A_2^{(1)})\) zero range process. (English) Zbl 1373.81244 Nucl. Phys., B 922, 148-185 (2017). MSC: 81R50 17B37 81V70 16T25 15B52 82C35 82C23 PDF BibTeX XML Cite \textit{A. Kuniba} and \textit{V. V. Mangazeev}, Nucl. Phys., B 922, 148--185 (2017; Zbl 1373.81244) Full Text: DOI arXiv OpenURL
Kuniba, Atsuo; Okado, Masato A \(q\)-boson representation of Zamolodchikov-Faddeev algebra for stochastic \(R\) matrix of \(U_q(A^{(1)}_n)\). (English) Zbl 1369.16033 Lett. Math. Phys. 107, No. 6, 1111-1130 (2017). MSC: 16T25 17B37 60J10 PDF BibTeX XML Cite \textit{A. Kuniba} and \textit{M. Okado}, Lett. Math. Phys. 107, No. 6, 1111--1130 (2017; Zbl 1369.16033) Full Text: DOI arXiv OpenURL
Orr, Daniel; Petrov, Leonid Stochastic higher spin six vertex model and \(q\)-TASEPs. (English) Zbl 1379.82016 Adv. Math. 317, 473-525 (2017). Reviewer: Guy Jumarie (Montréal) MSC: 82C20 82C22 82B23 60K35 PDF BibTeX XML Cite \textit{D. Orr} and \textit{L. Petrov}, Adv. Math. 317, 473--525 (2017; Zbl 1379.82016) Full Text: DOI arXiv OpenURL
Kuniba, Atsuo; Okado, Masato; Watanabe, Satoshi Integrable structure of multispecies zero range process. (English) Zbl 1367.81089 SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 044, 29 p. (2017). MSC: 81R50 60C99 17B37 16T25 81R12 15B52 PDF BibTeX XML Cite \textit{A. Kuniba} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 044, 29 p. (2017; Zbl 1367.81089) Full Text: DOI arXiv OpenURL
Garbali, Alexandr; de Gier, Jan; Wheeler, Michael A new generalisation of Macdonald polynomials. (English) Zbl 1360.05182 Commun. Math. Phys. 352, No. 2, 773-804 (2017). MSC: 05E05 PDF BibTeX XML Cite \textit{A. Garbali} et al., Commun. Math. Phys. 352, No. 2, 773--804 (2017; Zbl 1360.05182) Full Text: DOI arXiv OpenURL
Kuniba, Atsuo; Okado, Masato Matrix product formula for \(U_{q}(A_{2}^{(1)})\) -zero range process. (English) Zbl 1357.81122 J. Phys. A, Math. Theor. 50, No. 4, Article ID 044001, 20 p. (2017). MSC: 81R50 17B37 PDF BibTeX XML Cite \textit{A. Kuniba} and \textit{M. Okado}, J. Phys. A, Math. Theor. 50, No. 4, Article ID 044001, 20 p. (2017; Zbl 1357.81122) Full Text: DOI arXiv OpenURL
van Diejen, J. F.; Emsiz, E. Orthogonality of Bethe ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove. (English) Zbl 1360.82029 Commun. Math. Phys. 350, No. 3, 1017-1067 (2017). MSC: 82B23 82B20 PDF BibTeX XML Cite \textit{J. F. van Diejen} and \textit{E. Emsiz}, Commun. Math. Phys. 350, No. 3, 1017--1067 (2017; Zbl 1360.82029) Full Text: DOI arXiv OpenURL
Kuniba, A.; Mangazeev, V. V.; Maruyama, S.; Okado, M. Stochastic \(R\) matrix for \(\operatorname{U}_q(A_n^{(1)})\). (English) Zbl 1349.81115 Nucl. Phys., B 913, 248-277 (2016). MSC: 81R50 17B37 81R12 16T25 60J20 60J28 82C23 PDF BibTeX XML Cite \textit{A. Kuniba} et al., Nucl. Phys., B 913, 248--277 (2016; Zbl 1349.81115) Full Text: DOI arXiv OpenURL
Corwin, Ivan; Petrov, Leonid Stochastic higher spin vertex models on the line. (English) Zbl 1348.82055 Commun. Math. Phys. 343, No. 2, 651-700 (2016). Reviewer: Nasir N. Ganikhodjaev (Kuantan) MSC: 82C22 82C28 PDF BibTeX XML Cite \textit{I. Corwin} and \textit{L. Petrov}, Commun. Math. Phys. 343, No. 2, 651--700 (2016; Zbl 1348.82055) Full Text: DOI arXiv OpenURL
Wang, Dong; Waugh, David The transition probability of the \(q\)-TAZRP (\(q\)-bosons) with inhomogeneous jump rates. (English) Zbl 1338.82020 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 037, 16 p. (2016). MSC: 82B23 82C22 60J35 PDF BibTeX XML Cite \textit{D. Wang} and \textit{D. Waugh}, SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 037, 16 p. (2016; Zbl 1338.82020) Full Text: DOI arXiv OpenURL
Ferrari, Patrik L.; Vető, Bálint Tracy-Widom asymptotics for \(q\)-TASEP. (English. French summary) Zbl 1376.60080 Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 4, 1465-1485 (2015). MSC: 60K35 60B20 82B23 PDF BibTeX XML Cite \textit{P. L. Ferrari} and \textit{B. Vető}, Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 4, 1465--1485 (2015; Zbl 1376.60080) Full Text: DOI arXiv Euclid OpenURL
Corwin, Ivan; Petrov, Leonid The \(q\)-PushASEP: a New Integrable Model for Traffic in \(1+1\) dimension. (English) Zbl 1323.82029 J. Stat. Phys. 160, No. 4, 1005-1026 (2015). MSC: 82C22 60J75 82C31 90B20 33D52 PDF BibTeX XML Cite \textit{I. Corwin} and \textit{L. Petrov}, J. Stat. Phys. 160, No. 4, 1005--1026 (2015; Zbl 1323.82029) Full Text: DOI arXiv OpenURL
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz. (English) Zbl 1330.82017 Commun. Math. Phys. 339, No. 3, 1167-1245 (2015). Reviewer: Guy Jumarie (Montréal) MSC: 82B23 82C22 82B20 PDF BibTeX XML Cite \textit{A. Borodin} et al., Commun. Math. Phys. 339, No. 3, 1167--1245 (2015; Zbl 1330.82017) Full Text: DOI arXiv Link OpenURL
Barraquand, Guillaume A phase transition for \(q\)-TASEP with a few slower particles. (English) Zbl 1314.60153 Stochastic Processes Appl. 125, No. 7, 2674-2699 (2015). MSC: 60K35 60B20 PDF BibTeX XML Cite \textit{G. Barraquand}, Stochastic Processes Appl. 125, No. 7, 2674--2699 (2015; Zbl 1314.60153) Full Text: DOI arXiv OpenURL
Ayyer, Arvind; Schilling, Anne; Steinberg, Benjamin; Thiéry, Nicolas M. Directed nonabelian sandpile models on trees. (English) Zbl 1456.82607 Commun. Math. Phys. 335, No. 3, 1065-1098 (2015). MSC: 82C20 05C05 82C22 15A18 PDF BibTeX XML Cite \textit{A. Ayyer} et al., Commun. Math. Phys. 335, No. 3, 1065--1098 (2015; Zbl 1456.82607) Full Text: DOI arXiv OpenURL
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro Spectral theory for the \(q\)-boson particle system. (English) Zbl 1314.05212 Compos. Math. 151, No. 1, 1-67 (2015). Reviewer: Guy Jumarie (Montréal) MSC: 05E05 82B23 PDF BibTeX XML Cite \textit{A. Borodin} et al., Compos. Math. 151, No. 1, 1--67 (2015; Zbl 1314.05212) Full Text: DOI arXiv OpenURL
Pei, Yuchen A symmetry property for \(q\)-weighted Robinson-Schensted and other branching insertion algorithms. (English) Zbl 1303.05016 J. Algebr. Comb. 40, No. 3, 743-770 (2014). MSC: 05A30 05A05 05C20 05C85 05E10 05E05 PDF BibTeX XML Cite \textit{Y. Pei}, J. Algebr. Comb. 40, No. 3, 743--770 (2014; Zbl 1303.05016) Full Text: DOI arXiv OpenURL
van Diejen, J. F.; Emsiz, E. Diagonalization of the infinite \(q\)-boson system. (English) Zbl 1293.47071 J. Funct. Anal. 266, No. 9, 5801-5817 (2014). MSC: 47N20 82B20 47A40 82B23 PDF BibTeX XML Cite \textit{J. F. van Diejen} and \textit{E. Emsiz}, J. Funct. Anal. 266, No. 9, 5801--5817 (2014; Zbl 1293.47071) Full Text: DOI arXiv OpenURL
Korhonen, Marko; Lee, Eunghyun The transition probability and the probability for the left-most particle’s position of the \(q\)-totally asymmetric zero range process. (English) Zbl 1291.82086 J. Math. Phys. 55, No. 1, 013301, 15 p. (2014). MSC: 82C22 82C31 82B23 PDF BibTeX XML Cite \textit{M. Korhonen} and \textit{E. Lee}, J. Math. Phys. 55, No. 1, 013301, 15 p. (2014; Zbl 1291.82086) Full Text: DOI arXiv OpenURL
Borodin, Alexei; Corwin, Ivan Macdonald processes. (English) Zbl 1291.82077 Probab. Theory Relat. Fields 158, No. 1-2, 225-400 (2014). Reviewer: Guy Jumarie (Montréal) MSC: 82C22 82B23 60H15 33D52 PDF BibTeX XML Cite \textit{A. Borodin} and \textit{I. Corwin}, Probab. Theory Relat. Fields 158, No. 1--2, 225--400 (2014; Zbl 1291.82077) Full Text: DOI arXiv Link OpenURL
van Diejen, Jan Felipe; Emsiz, Erdal The semi-infinite \(q\)-boson system with boundary interaction. (English) Zbl 1292.81105 Lett. Math. Phys. 104, No. 1, 103-113 (2014). MSC: 81T25 81R50 81U15 33D52 PDF BibTeX XML Cite \textit{J. F. van Diejen} and \textit{E. Emsiz}, Lett. Math. Phys. 104, No. 1, 103--113 (2014; Zbl 1292.81105) Full Text: DOI arXiv OpenURL
Borodin, Alexei; Petrov, Leonid Integrable probability: from representation theory to MacDonald processes. (English) Zbl 1295.82023 Probab. Surv. 11, 1-58 (2014). MSC: 82C22 60J65 82D60 05B45 82-02 PDF BibTeX XML Cite \textit{A. Borodin} and \textit{L. Petrov}, Probab. Surv. 11, 1--58 (2014; Zbl 1295.82023) Full Text: DOI arXiv Euclid OpenURL
Lee, Eunghyun The current distribution of the multiparticle hopping asymmetric diffusion model. (English) Zbl 1259.82066 J. Stat. Phys. 149, No. 1, 50-72 (2012). MSC: 82C22 82B23 PDF BibTeX XML Cite \textit{E. Lee}, J. Stat. Phys. 149, No. 1, 50--72 (2012; Zbl 1259.82066) Full Text: DOI arXiv OpenURL
Lee, Eunghyun Transition probabilities of the Bethe ansatz solvable interacting particle systems. (English) Zbl 1213.82058 J. Stat. Phys. 142, No. 4, 643-656 (2011). MSC: 82C22 82B26 PDF BibTeX XML Cite \textit{E. Lee}, J. Stat. Phys. 142, No. 4, 643--656 (2011; Zbl 1213.82058) Full Text: DOI arXiv OpenURL
Dorlas, T. C.; Priezzhev, V. B. Finite-time current probabilities in the asymmetric exclusion process on a ring. (English) Zbl 1131.82024 J. Stat. Phys. 129, No. 4, 787-805 (2007). MSC: 82C22 PDF BibTeX XML Cite \textit{T. C. Dorlas} and \textit{V. B. Priezzhev}, J. Stat. Phys. 129, No. 4, 787--805 (2007; Zbl 1131.82024) Full Text: DOI OpenURL
Alimohammadi, Masoud Solvable reaction-diffusion processes without exclusion. (English) Zbl 1111.82037 J. Math. Phys. 47, No. 2, 023304, 12 p. (2006). MSC: 82C22 60K35 82C70 PDF BibTeX XML Cite \textit{M. Alimohammadi}, J. Math. Phys. 47, No. 2, 023304, 12 p. (2006; Zbl 1111.82037) Full Text: DOI arXiv OpenURL
Povolotsky, A. M.; Mendes, J. F. F. Bethe ansatz solution of discrete time stochastic processes with fully parallel update. (English) Zbl 1092.82036 J. Stat. Phys. 123, No. 1, 125-166 (2006). MSC: 82C41 82C20 82C32 PDF BibTeX XML Cite \textit{A. M. Povolotsky} and \textit{J. F. F. Mendes}, J. Stat. Phys. 123, No. 1, 125--166 (2006; Zbl 1092.82036) Full Text: DOI arXiv OpenURL
Alimohammadi, M.; Naimi, Y. Multispecies extension of the solvable partially asymmetric reaction-diffusion processes. (English) Zbl 1110.82031 J. Math. Phys. 46, No. 5, 053306, 16 p. (2005). MSC: 82C31 PDF BibTeX XML Cite \textit{M. Alimohammadi} and \textit{Y. Naimi}, J. Math. Phys. 46, No. 5, 053306, 16 p. (2005; Zbl 1110.82031) Full Text: DOI arXiv OpenURL