Laudatio - The Mathematical Work of Jürgen Gärtner - Hollander.- Part I The Parabolic Anderson Model.- The Parabolic Anderson Model with Long Range Basic Hamiltonian and Weibull Type Random Potential. S. Molchanov and H. Zhang.- Parabolic Anderson Model with Voter Catalysts: Dichotomy in the Behavior of Lyapunov Exponents. G. Maillard, T. Mountford and S. Schöpfer.- Precise Asymptotics for the Parabolic Anderson Model with a Moving Catalyst or Trap. A. Schnitzler and T. Wolff.- Parabolic Anderson Model with a Finite Number of Moving Catalysts. F. Castell, O. Gün and G. Maillard.- Survival Probability of a Random Walk Among a Poisson System of Moving Traps. A. Drewitz, J. Gärtner, A. F. Ramírez, R. Sun.- Quenched Lyapunov Exponent for the Parabolic Anderson Model in a Dynamic Random Environment. J. Gärtner, F. den Hollander and G. Maillard.- Asymptotic Shape and Propagation of Fronts for Growth Models in Dynamic Random Environment. H. Kesten, A.F. Ramírez and V. Sidoravicius.- The Parabolic Anderson Model with Acceleration and Deceleration. W. König and S. Schmidt.- A Scaling Limit Theorem for the Parabolic Anderson Model with Exponential Potential - H. Lacoin and P. Mörters.- Part II Self-interacting Random Walks and Polymers.- The strong Interaction Limit of Continuous-time Weakly Self-avoiding Walk. D. C. Brydges, A. Dahlqvist, and G. Slade.- Copolymers at Selective Interfaces: Settled Issues and Open Problems. F. Caravenna, G. Giacomin and F.L. Toninelli.- Some Locally Self-interacting Walks on the Integers. A. Erschler, B. Tóth and W. Werner.- Stretched Polymers in Random Environment. D. Ioffe and Y. Velenik.- Part III Branching Processes.- Multiscale Analysis: Fisher-Wright Diffusions with Rare Mutations and Selection, Logistic Branching System. D.A. Dawson and A. Greven.- Properties of States of Super-a-stable Motion with Branching of Index 1+ß. K. Fleischmann, L. Mytnik, and V Wachtel.- Part IV Miscellaneous Topics in Statistical Mechanics.- A Quenched Large Deviation Principle and a Parisi Formula for a Perceptron Version of the Grem. E. Bolthausen and N. Kistlerr.- Metastability: from Mean Field Models to SPDEs. A. Bovier.- Hydrodynamic Limit for the V f  Interface Model via Two-scale Approach. T. Funaki.- Statistical Mechanics on Isoradial Graphs. C. Boutillier and B. de Tilière.

Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues - one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world's leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.