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## Scaling for a one-dimensional directed polymer with boundary conditions

- T. Seppalainen
- Mathematics
- 12 November 2009

We study a 1 + 1-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights and both endpoints of the path fixed. Among directed polymers this… Expand

## Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process

- M. Balazs, E. Cator, T. Seppalainen
- Mathematics
- 13 March 2006

We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right… Expand

## Bounds for scaling exponents for a 1+1 dimensional directed polymer in a Brownian environment

- T. Seppalainen, Benedek Valk'o
- Mathematics
- 24 June 2010

We study the scaling exponents of a 1+1-dimensional directed polymer in a Brownian random environment introduced by O'Connell and Yor. For a version of the model with boundary conditions that are… Expand

## Tropical Combinatorics and Whittaker functions

- Ivan Corwin, N. O'Connell, T. Seppalainen, Nikos Zygouras
- Mathematics
- 16 October 2011

We establish a fundamental connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions, analogous to the well known relationship between the RSK correspondence and Schur… Expand

## Order of current variance and diffusivity in the asymmetric simple exclusion process

- M. Balazs, T. Seppalainen
- Mathematics
- 15 August 2006

We prove that the variance of the current across a characteristic is of order t 2/3 in a stationary asymmetric simple exclusion process, and that the diffusivity has order t 1/3. The proof proceeds… Expand

## Ratios of partition functions for the log-gamma polymer

- N. Georgiou, F. Rassoul-Agha, T. Seppalainen, A. Yilmaz
- Mathematics
- 6 March 2013

We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition in-… Expand

## Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks

- T. Seppalainen
- Physics, Mathematics
- 3 October 2003

Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n 1 / 2 one sees initial ﬂuctuations transported along characteristics and… Expand

## Joint distribution of Busemann functions in the exactly solvable corner growth model

- W. Fan, T. Seppalainen
- Mathematics
- 28 August 2018

We describe the joint distribution of the Busemann functions of the corner growth model with exponential weights. The marginals of this measure are identified as the unique spatially ergodic fixed… Expand

## SCALING EXPONENT FOR THE HOPF-COLE SOLUTION OF KPZ/STOCHASTIC BURGERS

- M. Balazs, J. Quastel, T. Seppalainen
- Mathematics
- 25 September 2009

AL¨ AINEN Abstract. We consider the stochastic heat equation @tZ = @ 2 x Z − Z u W on the real line, where u W is space-time white noise. h(t, x) = −log Z(t, x) is interpreted as a solution of the… Expand

## Fluctuation exponents for directed polymers in the intermediate disorder regime

- Gregorio R. Moreno Flores, T. Seppalainen, Benedek Valk'o
- Physics
- 2 December 2013

We derive exact fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate scaling regime. This regime corresponds to taking the inverse… Expand

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