On a Factorization Formula for the Partition Function of Directed Polymers.

We prove a factorization formula for the point-to-point partition function associated with a model of directed polymers on the space-time lattice . The polymers are subject to a random potential induced by independent identically distributed random variables and we consider the regime of weak disorder, where polymers behave diffusively. We show that when writing the quotient of the point-to-point partition function and the transition probability for the underlying random walk as the product of two point-to-line partition functions plus an error term, then, for large time intervals [0, ], the error term is small uniformly over starting points and endpoints in the sub-ballistic regime , where can be arbitrarily close to 1.

Point fields of last passage percolation and coalescing fractional Brownian motions.

We consider large-scale point fields which naturally appear in the context of the Kardar-Parisi-Zhang (KPZ) phenomenon. Such point fields are geometrical objects formed by points of mass concentration, and by shocks separating the sources of these points. We introduce similarly defined point fields for processes of coalescing fractional Brownian motions (cfBMs).

On end-point distribution for directed polymers and related problems for randomly forced Burgers equation.

In this paper, we study several problems related to the theory of randomly forced Burgers equation. Our numerical analysis indicates that despite the localization effects the quenched variance of the endpoint distribution for directed polymers in the strong disorder regime grows as the polymer length [Formula: see text]. We also present numerical results in support of the 'one force-one solution' principle.

Ballistic deposition patterns beneath a growing Kardar-Parisi-Zhang interface.

We consider a (1+1)-dimensional ballistic deposition process with next-nearest-neighbor interactions, which belongs to the Kardar-Parisi-Zhang (KPZ) universality class. The focus of our analysis is on the properties of structures appearing in the bulk of a growing aggregate: a forest of independent clusters separated by "crevices." Competition for growth (mutual screening) between different clusters results in "thinning" of this forest, i.

Particle dynamics inside shocks in Hamilton-Jacobi equations.

The characteristic curves of a Hamilton-Jacobi equation can be seen as action-minimizing trajectories of fluid particles. For non-smooth 'viscosity' solutions, which give rise to discontinuous velocity fields, this description is usually pursued only up to the moment when trajectories hit a shock and cease to minimize the Lagrangian action. In this paper we show that, for any convex Hamiltonian, there exists a uniquely defined canonical global non-smooth coalescing flow that extends particle trajectories and determines the dynamics inside shocks.