Download this PDF file Fullscreen Fullscreen Off
References
- Alberts, Tom; Khanin, Konstantin; Quastel, Jeremy. The continuum directed random polymer. J. Stat. Phys. 154 (2014), no. 1-2, 305--326. MR3162542
- Alberts, Tom; Khanin, Konstantin; Quastel, Jeremy. The intermediate disorder regime for directed polymers in dimension $1+1$. Ann. Probab. 42 (2014), no. 3, 1212--1256. MR3189070
- Tom Alberts, Kostya Khanin, and Jeremy Quastel, phThe intermediate disorder regime for directed polymers in dimension 1+1, Phys. Rev. Lett. 105 (2010), 090603.
- Amir, Gideon; Corwin, Ivan; Quastel, Jeremy. Probability distribution of the free energy of the continuum directed random polymer in $1+1$ dimensions. Comm. Pure Appl. Math. 64 (2011), no. 4, 466--537. MR2796514
- Auffinger, Antonio; Damron, Michael. A simplified proof of the relation between scaling exponents in first-passage percolation. Ann. Probab. 42 (2014), no. 3, 1197--1211. MR3189069
- Auffinger, Antonio; Damron, Michael. The scaling relation $\chi=2\xi-1$ for directed polymers in a random environment. ALEA Lat. Am. J. Probab. Math. Stat. 10 (2013), no. 2, 857--880. MR3141825
- Baik, Jinho; Deift, Percy; Johansson, Kurt. On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (1999), no. 4, 1119--1178. MR1682248
- Balzs, M.; Cator, E.; Seppäläinen, T. Cube root fluctuations for the corner growth model associated to the exclusion process. Electron. J. Probab. 11 (2006), no. 42, 1094--1132 (electronic). MR2268539
- Balázs, Márton; Komjáthy, Júlia; Seppäläinen, Timo. Microscopic concavity and fluctuation bounds in a class of deposition processes. Ann. Inst. Henri Poincar Probab. Stat. 48 (2012), no. 1, 151--187. MR2919202
- Márton Balázs, Jeremy Quastel, and Timo Seppäläinen, phFluctuation exponent of the KPZ/stochastic Burgers equation, J. Amer. Math. Soc. 24 (2011), no. 3, 683--708. MR2784327
- Balázs, Márton; Seppäläinen, Timo. Order of current variance and diffusivity in the asymmetric simple exclusion process. Ann. of Math. (2) 171 (2010), no. 2, 1237--1265. MR2630064
- Baryshnikov, Yu. GUEs and queues. Probab. Theory Related Fields 119 (2001), no. 2, 256--274. MR1818248
- Bernardin, Cédric. Fluctuations in the occupation time of a site in the asymmetric simple exclusion process. Ann. Probab. 32 (2004), no. 1B, 855--879. MR2039945
- Bertini, Lorenzo; Giacomin, Giambattista. Stochastic Burgers and KPZ equations from particle systems. Comm. Math. Phys. 183 (1997), no. 3, 571--607. MR1462228
- Borodin, Alexei; Corwin, Ivan. Macdonald processes. Probab. Theory Related Fields 158 (2014), no. 1-2, 225--400. MR3152785
- Borodin, Alexei; Corwin, Ivan; Ferrari, Patrik. Free energy fluctuations for directed polymers in random media in $1+1$ dimension. Comm. Pure Appl. Math. 67 (2014), no. 7, 1129--1214. MR3207195
- Borodin, Alexei; Corwin, Ivan; Remenik, Daniel. Log-gamma polymer free energy fluctuations via a Fredholm determinant identity. Comm. Math. Phys. 324 (2013), no. 1, 215--232. MR3116323
- Alexei Borodin, Ivan Corwin, and Tomohiro Sasamoto, phFrom duality to determinants for q-TASEP and ASEP, arXiv:1207.5035 (2012).
- Cator, Eric; Groeneboom, Piet. Second class particles and cube root asymptotics for Hammersley's process. Ann. Probab. 34 (2006), no. 4, 1273--1295. MR2257647
- Chatterjee, Sourav. The universal relation between scaling exponents in first-passage percolation. Ann. of Math. (2) 177 (2013), no. 2, 663--697. MR3010809
- Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo. Probabilistic analysis of directed polymers in a random environment: a review. Stochastic analysis on large scale interacting systems, 115--142, Adv. Stud. Pure Math., 39, Math. Soc. Japan, Tokyo, 2004. MR2073332
- Comets, Francis; Yoshida, Nobuo. Brownian directed polymers in random environment. Comm. Math. Phys. 254 (2005), no. 2, 257--287. MR2117626
- Corwin, Ivan. The Kardar-Parisi-Zhang equation and universality class. Random Matrices Theory Appl. 1 (2012), no. 1, 1130001, 76 pp. MR2930377
- Ivan Corwin and Alan Hammond, phKPZ line ensemble, arXiv:1312.2600 (2013).
- Corwin, Ivan; O'Connell, Neil; Sepplinen, Timo; Zygouras, Nikolaos. Tropical combinatorics and Whittaker functions. Duke Math. J. 163 (2014), no. 3, 513--563. MR3165422
- Ivan Corwin, Timo Seppäläinen, and Hao Shen, The strict-weak lattice polymer, arXiv:1409.1794 (2014).
- den Hollander, Frank. Random polymers. Lectures from the 37th Probability Summer School held in Saint-Flour, 2007. Lecture Notes in Mathematics, 1974. Springer-Verlag, Berlin, 2009. xiv+258 pp. ISBN: 978-3-642-00332-5 MR2504175
- Dufresne, Daniel. An affine property of the reciprocal Asian option process. Osaka J. Math. 38 (2001), no. 2, 379--381. MR1833627
- Gravner, Janko; Tracy, Craig A.; Widom, Harold. Limit theorems for height fluctuations in a class of discrete space and time growth models. J. Statist. Phys. 102 (2001), no. 5-6, 1085--1132. MR1830441
- Hairer, Martin. Solving the KPZ equation. Ann. of Math. (2) 178 (2013), no. 2, 559--664. MR3071506
- Henley, Christopher L.; Lipowsky, Reinhard. Interface roughening in two-dimensional quasicrystals. Phys. Rev. Lett. 59 (1987), no. 15, 1679--1682. MR0909444
- Johansson, Kurt. Shape fluctuations and random matrices. Comm. Math. Phys. 209 (2000), no. 2, 437--476. MR1737991
- K. Kardar, G. Parisi, and Y. Zhang, phDynamic scaling of growing interfaces, Phys. Rev. Lett. 56 (1986), 889--892.
- J. Krug and H. Spohn, phKinetic roughening of growing surfaces, Solids far from equilibrium (C. Godrèche, ed.), Collection Aléa-Saclay: Monographs and Texts in Statistical Physics, 1, Cambridge University Press, Cambridge, 1992, pp. 117--130.
- Landim, C.; Quastel, J.; Salmhofer, M.; Yau, H.-T. Superdiffusivity of asymmetric exclusion process in dimensions one and two. Comm. Math. Phys. 244 (2004), no. 3, 455--481. MR2034485
- Ledoux, M. Deviation inequalities on largest eigenvalues. Geometric aspects of functional analysis, 167--219, Lecture Notes in Math., 1910, Springer, Berlin, 2007. MR2349607
- G. Moreno Flores, J. Quastel, and D. Remenik, phKPZ scaling for directed polymers and q-TASEP, Preprint.
- Moriarty, J.; O'Connell, N. On the free energy of a directed polymer in a Brownian environment. Markov Process. Related Fields 13 (2007), no. 2, 251--266. MR2343849
- O'Connell, Neil. Directed polymers and the quantum Toda lattice. Ann. Probab. 40 (2012), no. 2, 437--458. MR2952082
- Neil O'Connell and Janosch Ortmann, phTracy-Widom asymptotics for a random polymer model with gamma-distributed weights, arXiv:1408.5326 (2014).
- O'Connell, Neil; Yor, Marc. Brownian analogues of Burke's theorem. Stochastic Process. Appl. 96 (2001), no. 2, 285--304. MR1865759
- Quastel, Jeremy; Valkó, Benedek. $t^ {1/3}$ Superdiffusivity of finite-range asymmetric exclusion processes on $\Bbb Z$. Comm. Math. Phys. 273 (2007), no. 2, 379--394. MR2318311
- Quastel, Jeremy; Valkó, Benedek. A note on the diffusivity of finite-range asymmetric exclusion processes on $\Bbb Z$. In and out of equilibrium. 2, 543--549, Progr. Probab., 60, Birkhuser, Basel, 2008. MR2477398
- Quastel, Jeremy; Valkó, Benedek. Diffusivity of lattice gases. Arch. Ration. Mech. Anal. 210 (2013), no. 1, 269--320. MR3073154
- Seppäläinen, Timo. Scaling for a one-dimensional directed polymer with boundary conditions. Ann. Probab. 40 (2012), no. 1, 19--73. MR2917766
- Seppäläinen, Timo; Valkó, Benedek. Bounds for scaling exponents for a $1+1$ dimensional directed polymer in a Brownian environment. ALEA Lat. Am. J. Probab. Math. Stat. 7 (2010), 451--476. MR2741194
- Herbert Spohn, phStochastic integrability and the KPZ equation, IAMP News Bulletin (2012), 5--9.
- Tracy, Craig A.; Widom, Harold. A Fredholm determinant representation in ASEP. J. Stat. Phys. 132 (2008), no. 2, 291--300. MR2415104
- Yau, Horng-Tzer. $(\log t)^ {2/3}$ law of the two dimensional asymmetric simple exclusion process. Ann. of Math. (2) 159 (2004), no. 1, 377--405. MR2052358
This work is licensed under a Creative Commons Attribution 3.0 License.