Related papers: Point-to-line polymers and orthogonal Whittaker fu…
We prove an identity in distribution between two kinds of partition functions for the log-gamma directed polymer model: (1) the point-to-point partition function in a quadrant, (2) the point-to-line partition function in an octant. As an…
We study the partition function of two versions of the continuum directed polymer in 1+1 dimension. In the full-space version, the polymer starts at the origin and is free to move transversally in the reals, and in the half-space version,…
We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric Robinson-Schensted-Knuth correspondence…
We consider the log-Gamma polymer in the half-space with bulk weights distributed as $\operatorname{Gamma}^{-1}(2\theta)$ and diagonal weights as $\operatorname{Gamma}^{-1}(\alpha+\theta)$ for $\theta>0$ and $\alpha>-\theta$. We show that…
We show that the reformulation of the geometric Robinson-Schensted-Knuth (gRSK) correspondence via local moves, introduced in \cite{OSZ14} can be extended to cases where the input matrix is replaced by more general polygonal,…
We consider the convergence of partition functions and endpoint density for the half-space directed polymer model in dimension $1+1$ in the intermediate disorder regime as considered for the full space model by Alberts, Khanin and Quastel…
We study the half-space log-gamma polymer model with stationary initial conditions. We derive exact formulas for the distribution of the partition function along the diagonal across the entire High density phase and Low density phase. We…
We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…
We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with…
We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…
A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of $d\times d$ inverse-Wishart random matrices, so that the model nicely generalizes the well-studied log-gamma…
We prove that the free energy of the half-space log-gamma polymer $N^{2/3+\delta}$ away from the boundary in the non-attractive regime converges to the directed landscape. Based on the convergence of the full-space log-gamma free energy to…
We study the directed polymer model in a bounded environment in weak disorder but without $L^2$-boundedness, specifically the speed of homogenization for the field $(W_n^{0,x})_{x\in\mathbb Z^d}$, where $W_n^{0,x}$ denotes the associated…
We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study…
A polymer folding model on the square lattice is constructed with attractive contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a dynamical random lattice, with freely fluctuating co-ordination number at each vertex,…
Last passage percolation and directed polymer models on $\mathbb Z^2$ are invariant under translation and certain reflections. When these models have an integrable structure coming from either the RSK correspondence or the geometric RSK…
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 functions. This gives rise to a natural family…
The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is…
In this paper, we consider four integrable models of directed polymers for which the free energy is known to exhibit KPZ fluctuations. A common framework for the analysis of these models was introduced in our recent work on the…
We propose a nonlinear $\sigma$-model in a curved space as a general integrable elliptic model. We construct its exact solutions and obtain energy estimates near the critical point. We consider the Pohlmeyer transformation in Euclidean…