zbMATH — the first resource for mathematics

Confinement of Brownian polymers under geometric area tilts. (English) Zbl 1466.60068
Summary: We consider confinement properties of families of non-colliding Brownian bridges above a hard wall, which are subject to geometrically growing self-potentials of tilted area type. The model is introduced in order to mimic level lines of \(2+1\) discrete Solid-On-Solid random interfaces above a hard wall.

60F17 Functional limit theorems; invariance principles
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
Full Text: DOI Euclid arXiv
[1] Milton Abramowitz and Irene A Stegun. Handbook of mathematical functions: with formulas, graphs, and mathematical tables, volume 55. Courier Corporation, 1965. · Zbl 0171.38503
[2] Folkmar Bornemann. On the scaling limits of determinantal point processes with kernels induced by Sturm-Liouville operators. SIGMA, Symmetry, Integrability and Geometry: Methods and Applications, 12(83):1-20, 2016. · Zbl 1347.15041
[3] Alexei Borodin, Ivan Corwin, Daniel Remenik, et al. Multiplicative functionals on ensembles of non-intersecting paths. In Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, volume 51, pages 28-58. Institut Henri Poincaré, 2015. · Zbl 1357.60012
[4] Jean Bricmont, A El Mellouki, and Jürg Fröhlich. Random surfaces in statistical mechanics: Roughening, rounding, wetting,... Journal of statistical physics, 42(5-6):743-798, 1986.
[5] Pietro Caputo, Eyal Lubetzky, Fabio Martinelli, Allan Sly, and Fabio Lucio Toninelli. Dynamics of \((2+ 1) \)-dimensional SOS surfaces above a wall: Slow mixing induced by entropic repulsion. The Annals of Probability, 42(4):1516-1589, 2014. · Zbl 1311.60114
[6] Pietro Caputo, Eyal Lubetzky, Fabio Martinelli, Allan Sly, and Fabio Lucio Toninelli. Scaling limit and cube-root fluctuations in SOS surfaces above a wall. Journal of the European Mathematical Society, 18(5):931-995, 2016. · Zbl 1344.60091
[7] Earl A Coddington and Norman Levinson. Theory of ordinary differential equations. Tata McGraw-Hill Education, 1955. · Zbl 0064.33002
[8] Ivan Corwin and Evgeni Dimitrov. Transversal fluctuations of the asep, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles. Communications in Mathematical Physics, pages 1-67, 2018. · Zbl 1401.60176
[9] Ivan Corwin and Alan Hammond. Brownian Gibbs property for Airy line ensembles. Inventiones mathematicae, 195(2):441-508, 2014. · Zbl 1459.82117
[10] Maurice Duits. On global fluctuations for non-colliding processes. The Annals of Probability, 46(3):1279-1350, 2018. · Zbl 1429.60072
[11] Patrik L Ferrari and Herbert Spohn. Step fluctuations for a faceted crystal. Journal of statistical physics, 113(1-2):1-46, 2003. · Zbl 1116.82331
[12] Patrik L Ferrari, Herbert Spohn, et al. Constrained Brownian motion: fluctuations away from circular and parabolic barriers. The Annals of Probability, 33(4):1302-1325, 2005. · Zbl 1082.60071
[13] Dmitry Ioffe and Senya Shlosman. Formation of facets for an effective model of crystal growth. arXiv preprintarXiv:1704.06760, 2017. · Zbl 1173.82311
[14] Dmitry Ioffe, Senya Shlosman, and Fabio Lucio Toninelli. Interaction versus entropic repulsion for low temperature Ising polymers. Journal of Statistical Physics, 158(5):1007-1050, 2015. · Zbl 1321.82014
[15] Dmitry Ioffe, Senya Shlosman, and Yvan Velenik. An invariance principle to Ferrari-Spohn diffusions. Communications in Mathematical Physics, 336(2):905-932, 2015. · Zbl 1323.60055
[16] Dmitry Ioffe and Yvan Velenik. Low-temperature interfaces: Prewetting, layering, faceting and Ferrari-Spohn diffusions. Mark. Proc. Rel. Fields, 24:487-537, 2018. · Zbl 1414.60079
[17] Dmitry Ioffe, Yvan Velenik, and Vitali Wachtel. Dyson Ferrari-Spohn diffusions and ordered walks under area tilts. Probability Theory and Related Fields, pages 1-37, 2016. · Zbl 1405.60146
[18] Kurt Johansson. Random matrices and determinantal processes. In Mathematical Statistical Physics, Session LXXXIII: Lecture Notes of the Les Houches Summer School, 2005. · Zbl 1411.60144
[19] Kurt Johansson. Edge fluctuations of limit shapes. preprintarXiv:1704.06035, 2017. · Zbl 1423.60167
[20] Hubert Lacoin. Wetting and layering for solid-on-solid I: Identification of the wetting point and critical behavior. Communications in Mathematical Physics, pages 1-42, 2017. · Zbl 1398.82023
[21] Pascal Maillard and Ofer Zeitouni. Slowdown in branching brownian motion with inhomogeneous variance. Annales de l’Institut Henri Poincare, Probabilites et Statistiques, 52(3):1144-1160, 2016. · Zbl 1366.60105
[22] Roberto H Schonmann and Senya B Shlosman. Constrained variational problem with applications to the Ising model. Journal of statistical physics, 83(5-6):867-905, 1996. · Zbl 1081.82547
[23] Herbert Spohn. Kardar-Parisi-Zhang equation in one dimension and line ensembles. Pramana, 64(6):847-857, 2005.
[24] Yvan Velenik. Entropic repulsion of an interface in an external field. Probability theory and related fields, 129(1):83-112, 2004. · Zbl 1078.60088
[25] Thomas Weiss, Patrik Ferrari, and Herbert Spohn. Reflected Brownian motions in the KPZ universality class. Springer, 2017. · Zbl 1366.82004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.