Related papers: Temporal correlation in the inverse-gamma polymer
We study the long-range directed polymer model on $\mathbbm{Z}$ in a random environment, where the underlying random walk lies in the domain of attraction of an $\alpha$-stable process for some $\alpha\in(0,2]$. Similar to the more classic…
We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Bl\"ote and Nienhuis in J. Phys. A. {\bf 22}, 1415 (1989) and it describes polymers with some attraction, providing thus…
We analyze the freezing and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in…
We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar's solution obtained originally for a…
We study asymptotics of the free energy for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is given by Bernoulli variables. We first establish the existence and continuity of…
Systems of highly degenerate ordered or frozen state may exhibit inverse melting (reversible crystallization upon heating) or inverse freezing (reversible glass transition upon heating). This phenomena is reviewed, and a list of…
We study the connection between polymers at the theta temperature on the lattice and Schramm-Loewner chains with constant step length in the continuum. The latter realize a useful algorithm for the exact sampling of tricritical polymers,…
We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…
We study the free energy and its relevant quantity for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is given by the Bernoulli variables. We first establish the concentration…
Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice…
We introduce a new disorder regime for directed polymers with one space and one time dimension that is accessed by scaling the inverse temperature parameter \beta with the length of the polymer n. We scale \beta_n := \beta n^{-\alpha} for…
We present the first direct ab-initio computation of unequal-time correlation functions in non-Abelian lattice gauge theory. We demonstrate non-trivial consistency relations among correlators, time-translation invariance, and agreement with…
In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse…
The dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the model for coupling parameter g=1 (i.e., not in the weak coupling regime), and prove closeness of the time…
Polymer rings in solution are either permanently entangled or not. Permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume. Conversely,…
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,…
Half-space directed polymers in random environments are models of interface growth in the presence of an attractive hard wall. They arise naturally in the study of wetting and entropic repulsion phenomena. In 1985, Kardar predicted a…
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…
We define a lattice model for the interaction of a polymer with water. We solve the model in a suitable approximation. In the case of a non-polar homopolymer, for reasonable values of the parameters, the polymer is found in a non-compact…
We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…