An invariance principle to Ferrari-Spohn diffusions

DOI10.1007/s00220-014-2277-5zbMath1323.60055arXiv1403.5073OpenAlexW3099366873MaRDI QIDQ2018310

Senya B. Shlosman, Dimitry Ioffe, Yvan Velenik

Publication date: 14 April 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5073

zbMATH Keywords

scaling limitinvariance principleIsing modelstatistical physicsGibbs random fieldsSOS modelFerrari-Spohn diffusionstilted random walk bridge

Mathematics Subject Classification ID

Random fields (60G60) Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60) Applications of statistics to physics (62P35) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27) Functional limit theorems; invariance principles (60F17) Applications of functional analysis in probability theory and statistics (46N30)

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Cites Work

• An invariance principle for random walk bridges conditioned to stay positive
• Finite size scaling of the dynamical free-energy in a kinetically constrained model
• The shape of the \((2+1)\)D SOS surface above a wall
• Invariance principles for random walks conditioned to stay positive
• Walks, walls, wetting, and melting
• Constrained variational problem with applications to the Ising model.
• Universality of critical behaviour in a class of recurrent random walks
• Entropic repulsion of an interface in an external field
• On conditioning a random walk to stay nonnegative
• Constrained Brownian motion: fluctuations away from circular and parabolic barriers
• Finite connections for supercritical Bernoulli bond percolation in 2D
• Wiener – hopf factorization revisited and some applications
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