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- Herbert Spohn
- 2006

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy-Widom distribution of the largest eigenvalue of a GUE… (More)

We extend the work of Kurchan on the Gallavotti-Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes. These include jump processes describing the evolution of stochastic lattice gases driven in the bulk or through particle reservoirs, general diffusive processes in physical and/or velocity… (More)

The time-integrated current of the TASEP has non-Gaussian fluctuations of order t. The recently discovered connection to random matrices and the Painlevé II RiemannHilbert problem provides a technique through which we obtain the probability distribution of the current fluctuations, in particular their dependence on initial conditions, and the stationary… (More)

We determine the stationary two-point correlation function of the onedimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a… (More)

- Herbert Spohn
- 1999

Preface By intention, my project has two parts. The first one covers the classical electron theory. It is essentially self–contained and will be presented in the following chapters. 75 years after the discovery of quantum mechanics, to discuss only the classical version of the theory looks somewhat obsolete, in particular since many phenomena, like the… (More)

For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for self-similar growth from a single seed the universal distribution is the Tracy-Widom distribution from the theory of random matrices and that for growth from a flat… (More)

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli ρ measure as initial conditions, 0 < ρ < 1, is stationary in space and time. Let Nt(j) be the number of particles which have crossed the bond from j to j + 1 during the time span [0, t]. For j = (1− 2ρ)t+2w(ρ(1− ρ))1/3t2/3 we prove that the fluctuations… (More)

We prove that Nelson’s massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not unitarily equivalent with the Hamiltonian obtained from Euclidean quantization. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state… (More)

We study the large scale space–time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space–time scale these fluctuations are governed by an infinite-dimensional Ornstein–Uhlenbeck process. Its effective diffusion type covariance… (More)

- Tomohiro Sasamoto, Herbert Spohn
- Physical review letters
- 2010

We report on the first exact solution of the Kardar-Parisi-Zhang (KPZ) equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for the probability distribution function of the height h(x,t) for all t>0. In particular, we show… (More)