@incollection{joh08, AUTHOR = {Johansson, K.}, TITLE = {On some special directed last-passage percolation models}, BOOKTITLE = {Integrable systems and random matrices}, SERIES = {Contemp. Math.}, VOLUME = {458}, PAGES = {333--346}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2008}, } @article{bor99, AUTHOR = {Borodin, A.}, TITLE = {Biorthogonal ensembles}, JOURNAL = {Nuclear Phys. B}, FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and Experimental High Energy Physics. Quantum Field Theory and Statistical Systems}, VOLUME = {536}, YEAR = {1999}, NUMBER = {3}, PAGES = {704--732}, } @article{tw94_bessel, AUTHOR = {Tracy, C. A. and Widom, H.}, TITLE = {Level spacing distributions and the {B}essel kernel}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {161}, YEAR = {1994}, NUMBER = {2}, PAGES = {289--309}, } @article{fr05, AUTHOR = {Forrester, P. J. and Rains, E. M.}, TITLE = {Interpretations of some parameter dependent generalizations of classical matrix ensembles}, JOURNAL = {Probab. Theory Related Fields}, FJOURNAL = {Probability Theory and Related Fields}, VOLUME = {131}, YEAR = {2005}, NUMBER = {1}, PAGES = {1--61}, } @article{tw94_airy, AUTHOR = {Tracy, C. A. and Widom, H.}, TITLE = {Level-spacing distributions and the {A}iry kernel}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {159}, YEAR = {1994}, NUMBER = {1}, PAGES = {151--174}, } @Article{joh07, author = {Johansson, K.}, title = {From {G}umbel to {T}racy--{W}idom}, journal = {Probab. Theory and Related Fields}, fjournal = {Probability Theory and Related Fields}, year = {2007}, volume = {138}, number = {1}, pages = {75--112}, eprint = {arXiv:math/0510181 [math.PR]}, } @article{mut95, AUTHOR = {Muttalib, K. A.}, TITLE = {Random matrix models with additional interactions}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and General}, VOLUME = {28}, YEAR = {1995}, NUMBER = {5}, PAGES = {L159--L164}, } @article{for93, AUTHOR = {Forrester, P. J.}, TITLE = {The spectrum edge of random matrix ensembles}, JOURNAL = {Nuclear Phys. B}, FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and Experimental High Energy Physics. Quantum Field Theory and Statistical Systems}, VOLUME = {402}, YEAR = {1993}, NUMBER = {3}, PAGES = {709--728}, } @article{vy06, AUTHOR = {Vershik, A. and Yakubovich, Yu.}, TITLE = {Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {261}, YEAR = {2006}, NUMBER = {3}, PAGES = {759--769}, } @article{ver97, AUTHOR = {Vershik, A. M.}, TITLE = {Limit distribution of the energy of a quantum ideal gas from the point of view of the theory of partitions of natural numbers}, JOURNAL = {Uspekhi Mat. Nauk}, FJOURNAL = {Uspekhi Matematicheskikh Nauk}, VOLUME = {52}, YEAR = {1997}, NUMBER = {2(314)}, PAGES = {139--146}, EPRINT = {http://www.mathnet.ru/links/65773fba011d9338ef739b43fded1dd2/rm823.pdf}, } @article{km19, AUTHOR = {Kuijlaars, A. B. J. and Molag, L. D.}, TITLE = {The local universality of {M}uttalib--{B}orodin biorthogonal ensembles with parameter {$\theta=\frac 12$}}, JOURNAL = {Nonlinearity}, FJOURNAL = {Nonlinearity}, VOLUME = {32}, YEAR = {2019}, NUMBER = {8}, PAGES = {3023--3081}, } @article{mol20, AUTHOR = {Molag, L. D.}, EPRINT = {2003.11299}, EPRINTTYPE = {arXiv}, TITLE = {The local universality of {M}uttalib--{B}orodin ensembles when the parameter {$\theta$} is the reciprocal of an integer}, year = {2020}, } @article{bgs19, author = {Borodin, A. and Gorin, V. and Strahov, E.}, title = {Product matrix processes as limits of random plane partitions}, journal = {International Mathematics Research Notices}, year = {2019}, month = {01}, } @article{fox61, author = {Fox, C.}, journal = {Transactions of the American Mathematical Society}, number = {3}, pages = {395--429}, publisher = {American Mathematical Society}, title = {The {G} and {H} Functions as Symmetrical {F}ourier Kernels}, volume = {98}, year = {1961} } @misc{nist, key = "{\relax DLMF}", title = "{\it NIST Digital Library of Mathematical Functions}", howpublished = "http://dlmf.nist.gov/, Release 1.0.28 of 2020-09-15", url = "http://dlmf.nist.gov/", note = "F.~W.~J. Olver, A.~B. {Olde Daalhuis}, D.~W. Lozier, B.~I. Schneider, R.~F. Boisvert, C.~W. Clark, B.~R. Miller, B.~V. Saunders, H.~S. Cohl, and M.~A. McClain, eds." } @Article{joh00, AUTHOR = {Johansson, K.}, TITLE = {Shape fluctuations and random matrices}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {209}, YEAR = {2000}, NUMBER = {2}, PAGES = {437--476}, } @Article{or03, Title = {{C}orrelation function of {S}chur process with application to local geometry of a random 3--dimensional {Y}oung diagram}, Author = {Okounkov, A. and Reshetikhin, N.}, Journal = {J. Amer. Math. Soc.}, Year = {2003}, Number = {3}, Pages = {581--603 (electronic)}, Volume = {16}, Fjournal = {Journal of the American Mathematical Society}, } @Article{or07, Title = {{R}andom skew plane partitions and the {P}earcey process}, Author = {Okounkov, A. and Reshetikhin, N.}, Journal = {Comm. Math. Phys.}, Year = {2007}, Number = {3}, Pages = {571--609}, Volume = {269}, Fjournal = {Communications in Mathematical Physics}, } @article{ck01, Author = {Cerf, R. and Kenyon, R.}, Fjournal = {Communications in Mathematical Physics}, Journal = {Comm. Math. Phys.}, Number = {1}, Pages = {147--179}, Title = {The low-temperature expansion of the {W}ulff crystal in the 3{D} {I}sing model}, Volume = {222}, Year = {2001}, } @article{bnh84, Author = {Nienhuis, B. and Hilhorst, H. J. and Bl{\"o}te, H. W. J.}, Fjournal = {Journal of Physics. A. Mathematical and General}, Journal = {J. Phys. A}, Number = {18}, Pages = {3559--3581}, Title = {Triangular {SOS} models and cubic-crystal shapes}, Volume = {17}, Year = {1984}, } @article{bf03, year = 2003, publisher = {{IOP} Publishing}, volume = {36}, number = {12}, pages = {2963--2981}, author = {Borodin, A. and Forrester, P. J.}, title = {Increasing subsequences and the hard-to-soft edge transition in matrix ensembles}, journal = {Journal of Physics A: Mathematical and General}, } @Book{rom15, title = {The Surprising Mathematics of Longest Increasing Subsequences}, publisher = {Cambridge University Press}, year = {2015}, author = {Romik, D.}, } @Article{bb19, author = {Betea, D. and Bouttier, J.}, title = {The Periodic {S}chur Process and Free Fermions at Finite Temperature}, journal = {Math. Phys. Anal. Geom.}, year = {2019}, volume = {22}, number = {1}, pages = {22:3}, fjournal = {Mathematical Physics, Analysis and Geometry. An International Journal Devoted to the Theory and Applications of Analysis and Geometry to Physics}, } @article {bor10, AUTHOR = {Bornemann, F.}, TITLE = {On the numerical evaluation of {F}redholm determinants}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {79}, YEAR = {2010}, NUMBER = {270}, PAGES = {871--915}, } @ARTICLE{bfo20, author = "Betea, D. and Ferrari, P.L. and Occelli, A.", title = "Stationary half-space last passage percolation", journal = "Comm. Math. Phys.", fjournal = "Communications in Mathematical Physics", year = "2020", volume = "377", issue = "1", PAGES = "421--467", } @book{bat, author = "Bateman, H. and Erd{\'e}lyi, A. and Magnus, W. and Oberhettinger, F. and Tricomi, F. G.", title = "{Higher transcendental functions}", publisher = "McGraw-Hill", address = "New York, NY", series = "California Institute of Technology Bateman Manuscript Project", year = "1955", url = "https://authors.library.caltech.edu/43491/", } @book{mac, Address = {New York}, Author = {Macdonald, I. G.}, Edition = {Second edition}, Pages = {x+475}, Publisher = {Oxford University Press}, Title = {{S}ymmetric functions and {H}all polynomials}, Year = {1995} } @article{oko01, Author = {Okounkov, A.}, Fjournal = {Selecta Mathematica. New Series}, Journal = {Selecta Math. (N.S.)}, Number = {1}, Pages = {57--81}, Title = {{I}nfinite wedge and random partitions}, Volume = {7}, Year = {2001}, } @Article{bbbccv18, author = {Betea, D. and Boutillier, C. and Bouttier, J. and Chapuy, G. and Corteel, S. and Vuleti\'c, M.}, title = {{P}erfect sampling algorithm for {S}chur processes}, journal = {Markov Processes Relat. Fields}, year = {2018}, volume = {24}, pages = {381-418}, } @Article{b18, author = {Betea, D.}, title = {On the combinatorics of last passage percolation in a quarter square and {$GOE^2$} fluctuations}, year = {2018}, eprint = {arXiv:1809.06792 [math-ph]}, } @article{bor11, title = "Schur dynamics of the Schur processes", journal = "Adv. Math.", fjournal = "Advances in Mathematics", volume = "228", number = "4", pages = "2268 - 2291", year = "2011", author = "Borodin, A.", } @article{kra06, Author = {Krattenthaler, C.}, Journal = {Adv. Appl. Math.}, Number = {3}, Pages = {404--431}, Title = {{G}rowth diagrams, and increasing and decreasing chains in fillings of {F}errers shapes}, Volume = {37}, Year = {2006}, } @book{ful97, AUTHOR = {Fulton, W.}, TITLE = {Young tableaux}, SERIES = {London Mathematical Society Student Texts}, VOLUME = {35}, NOTE = {With applications to representation theory and geometry}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1997}, PAGES = {x+260}, } @article {gre74, AUTHOR = {Greene, C.}, TITLE = {An extension of {S}chensted's theorem}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {14}, YEAR = {1974}, PAGES = {254--265}, } @article{bur74, AUTHOR = {Burge, W. H.}, TITLE = {Four correspondences between graphs and generalized {Y}oung tableaux}, JOURNAL = {J. Combinatorial Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {17}, YEAR = {1974}, PAGES = {12--30}, } @article{knu70, author = "Knuth, D. E.", fjournal = "Pacific Journal of Mathematics", journal = "Pacific J. Math.", number = "3", pages = "709--727", publisher = "Pacific Journal of Mathematics, A Non-profit Corporation", title = "Permutations, matrices, and generalized Young tableaux.", volume = "34", year = "1970" } @article {fom86, AUTHOR = {Fomin, S.}, TITLE = {The generalized {R}obinson-{S}chensted-{K}nuth correspondence}, JOURNAL = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)}, FJOURNAL = {Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta imeni V. A. Steklova Akademii Nauk SSSR (LOMI)}, VOLUME = {155}, YEAR = {1986}, NUMBER = {Differentsial'naya Geometriya, Gruppy Li i Mekh. VIII}, PAGES = {156--175, 195}, } @article{fom95, AUTHOR = {Fomin, S.}, TITLE = {Schur operators and {K}nuth correspondences}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {72}, YEAR = {1995}, NUMBER = {2}, PAGES = {277--292}, } @article{pm17, AUTHOR = {Matveev, K. and Petrov, L.}, TITLE = {{$q$}-randomized {R}obinson-{S}chensted-{K}nuth correspondences and random polymers}, JOURNAL = {Ann. Inst. Henri Poincar\'e D}, FJOURNAL = {Annales de l'Institut Henri Poincar\'e D. Combinatorics, Physics and their Interactions}, VOLUME = {4}, YEAR = {2017}, NUMBER = {1}, PAGES = {1--123}, } @article{bp16, title = "Nearest neighbor {M}arkov dynamics on {M}acdonald processes", journal = "Adv. in Math.", fjournal = "Advances in Mathematics", volume = "300", pages = "71 - 155", year = "2016", note = "Special volume honoring Andrei Zelevinsky", issn = "0001-8708", author = "Borodin, A. and Petrov, L.", } @article{bcgr20, author = {Bisi, E. and Cunden, F. D. and Gibbons, S. and Romik, D.}, title = {Sorting networks, staircase {Y}oung tableaux, and last passage percolation}, journal = {S\'em. Lothar. Combin.}, year = {2020}, volume = {84B}, pages = {Art. 3, 12}, fjournal = {S\'eminaire Lotharingien de Combinatoire}, } @Article{boz20, author = {Bisi, E. and O'Connell, N. and Zygouras, N.}, title = {The geometric {B}urge correspondence and the partition function of polymer replicas}, year = {2020}, eprint = {arXiv:2001.09145 [math.PR]}, } @Article{bo20, author = {Betea, D. and Occelli, A.}, title = {Discrete and continuous Muttalib--Borodin processes I: the hard edge}, year = {2020}, eprint = {2010.15529}, eprinttype = {arXiv}, } @incollection {ny04, AUTHOR = {Noumi, M. and Yamada, Y.}, TITLE = {Tropical {R}obinson--{S}chensted--{K}nuth correspondence and birational {W}eyl group actions}, BOOKTITLE = {Representation theory of algebraic groups and quantum groups}, SERIES = {Adv. Stud. Pure Math.}, VOLUME = {40}, PAGES = {371--442}, PUBLISHER = {Math. Soc. Japan, Tokyo}, YEAR = {2004}, } @incollection {kir01, AUTHOR = {Kirillov, A. N.}, TITLE = {Introduction to tropical combinatorics}, BOOKTITLE = {Physics and combinatorics, 2000 ({N}agoya)}, PAGES = {82--150}, PUBLISHER = {World Sci. Publ., River Edge, NJ}, YEAR = {2001}, } @article {cosz14, AUTHOR = {Corwin, I. and O'Connell, N. and Sepp\"{a}l\"{a}inen, T. and Zygouras, N.}, TITLE = {Tropical combinatorics and {W}hittaker functions}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {163}, YEAR = {2014}, NUMBER = {3}, PAGES = {513--563}, } @article {osz14, AUTHOR = {O'Connell, N. and Sepp\"{a}l\"{a}inen, T. and Zygouras, N.}, TITLE = {Geometric {RSK} correspondence, {W}hittaker functions and symmetrized random polymers}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {197}, YEAR = {2014}, NUMBER = {2}, PAGES = {361--416}, } @Article{bcf14, author = {Borodin, A. and Corwin, I. and Ferrari, P.}, title = {Free Energy Fluctuations for Directed Polymers in Random Media in $1 + 1$ Dimension}, journal = {Communications on Pure and Applied Mathematics}, year = {2014}, volume = {67}, number = {7}, pages = {1129--1214}, } @article{or06, Author = {Okounkov, A. and Reshetikhin, N.}, Fjournal = {Moscow Mathematical Journal}, Journal = {Mosc. Math. J.}, Number = {3}, Pages = {553--566, 588}, Title = {{T}he birth of a random matrix}, Volume = {6}, Year = {2006} } @article{bbnv18, author = {Betea, D. and Bouttier, J. and Nejjar, P. and Vuleti\'c, M.}, title = {The free boundary {S}chur process and applications {I}}, journal = {Ann. Henri Poincar\'e}, year = {2018}, volume = {19}, number = {12}, pages = {3663--3742}, } @article{bar01, AUTHOR = {Baryshnikov, Yu.}, TITLE = {G{UE}s and queues}, JOURNAL = {Probab. Theory Related Fields}, FJOURNAL = {Probability Theory and Related Fields}, VOLUME = {119}, YEAR = {2001}, NUMBER = {2}, PAGES = {256--274}, } @article{aik13, title = {Products of rectangular random matrices: Singular values and progressive scattering}, author = {Akemann, G. and Ipsen, J. R. and Kieburg, M.}, journal = {Phys. Rev. E}, volume = {88}, issue = {5}, pages = {052118}, numpages = {13}, year = {2013}, month = {Nov}, } @article{kz14, AUTHOR = {Kuijlaars, Arno B. J. and Zhang, Lun}, TITLE = {Singular values of products of {G}inibre random matrices, multiple orthogonal polynomials and hard edge scaling limits}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {332}, YEAR = {2014}, NUMBER = {2}, PAGES = {759--781}, } @article{bgs14, AUTHOR = {Bertola, M. and Gekhtman, M. and Szmigielski, J.}, TITLE = {Cauchy-{L}aguerre two-matrix model and the {M}eijer-{G} random point field}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {326}, YEAR = {2014}, NUMBER = {1}, PAGES = {111--144}, } @article {bg15, AUTHOR = {Borodin, A. and Gorin, V.}, TITLE = {General {$\beta$}-{J}acobi corners process and the {G}aussian free field}, JOURNAL = {Comm. Pure Appl. Math.}, FJOURNAL = {Communications on Pure and Applied Mathematics}, VOLUME = {68}, YEAR = {2015}, NUMBER = {10}, PAGES = {1774--1844}, }