A martingale approach to directed polymers in a random environment

DOI10.1007/BF02213739zbMath0837.60069OpenAlexW2053709978MaRDI QIDQ1908210

Sergio A. Albeverio, Xian Yin Zhou

Publication date: 20 May 1996

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02213739

zbMATH Keywords

Wiener processrandom walksmartingalesdirected polymersrandom environment

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Statistical mechanics of polymers (82D60)

Related Items (17)

Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive ⋮ Directed polymers in random environment are diffusive at weak disorder ⋮ Strong localization and macroscopic atoms for directed polymers ⋮ The endpoint distribution of directed polymers ⋮ New bounds for the free energy of directed polymers in dimension \(1+1\) and \(1+2\) ⋮ Joint localization of directed polymers ⋮ Central limit theorems for the \((2 + 1)\)-dimensional directed polymer in the weak disorder limit ⋮ Coincidence of Lyapunov exponents for random walks in weak random potentials ⋮ Superdiffusivity for a Brownian polymer in a continuous Gaussian environment ⋮ A PDE hierarchy for directed polymers in random environments ⋮ Almost sure exponential behavior of a directed polymer in a fractional Brownian environment ⋮ Fluctuation exponents and large deviations for directed polymers in a random environment ⋮ Convergence of the law of the environment seen by the particle for directed polymers in random media in the \(L^{2}\) region ⋮ On the Brownian-directed polymer in a Gaussian random environment ⋮ Directed polymer in \(\gamma\)-stable random environments ⋮ Localization of directed polymers in continuous space ⋮ A remark on diffusion of directed polymers in random environments

Cites Work

• On the speed of convergence in first-passage percolation
• First passage percolation for random colorings of \(\mathbb{Z}^ d\)
• A note on the diffusion of directed polymers in a random environment
• Divergence of shape fluctuations in two dimensions
• Diffusion of directed polymers in a random environment.
• Polymers on disordered trees, spin glasses, and traveling waves.
• Fluctuations of extensive functions of quenched random couplings
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