A dynamic one-dimensional interface interacting with a wall

硬壁上方的动态界面与半直线上的反射随机偏微分方程

Dynamical interface above a hard wall and reflected SPDE on the half-line

研究硬壁上方带原点钉扎的角翻转随机界面，在扩散尺度下证明其平稳涨落收敛到半直线反射随机热方程，并得到三维贝塞尔过程为该SPDE的不变测度。

Metastability for expanding bubbles on a sticky substrate

We study the dynamical behavior of a one dimensional interface interacting with a sticky unpenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contact between the interface and the substrate are given an energetic bonus while an external force with constant intensity pulls the interface away from the wall. Our interface is modeled by the graph of a one-dimensional nearest-neighbor path on $\mathbb{Z}_+$, starting at $0$ and ending at $0$ after $2N$ steps, the wall corresponding to level-zero the horizontal axis. At equilibrium each path $ξ=(ξ_x)_…

Surface transition in the collapsed phase of a self-interacting walk adsorbed along a hard wall

The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plan and interacting with the horizontal axis. The model has been introduced in \cite{F90} to investigate the behavior of a homopolymer dipped in a poor solvent and adsorbed along a horizontal hard wall. It is known to undergo a collapse transition between an extended phase, inside which typical configurations of the polymer have a large horizontal extension (comparable to their total size), and a collapsed phase inside which the polymer looks like a glo…

On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature

We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $Λ$, both under the infinite volume measure and under the measure with zero boundary conditions around $Λ$, this probability turns out to behave like $\exp(-τ_β(0) L \log L )$, with $τ_β(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.

Dynamic entropic repulsion for interacting interfaces

The dynamic entropic repulsion for the Ginzburg-Landau $\nablaϕ$ interface model was discussed in [Deuschel-N. 2007] and the asymptotics of the height of the interface was identified. This paper studies a similar problem for two interfaces on the wall which are interacting with one another by the exclusion rule. Each leading order of the asymptotics of height is $\sqrt{\log t}$ as $t\to\infty$ for the system on $\integer^d,\,d\ge3$, $\log t$ for the system on $\integer^2$. The coefficient of the leading term for each interface is also identified.

受垂直壁吸引的相互作用部分有向自回避行走的相图

Phase diagram of the interacting partially directed self-avoiding walk attracted by a vertical wall

本文研究受垂直壁吸引的相互作用部分有向自回避行走，证明塌缩相内存在表面转变，并给出配分函数的精确渐近，严格证实了物理学家的猜想。

Harmonically confined long-ranged interacting gas in the presence of a hard wall

In this paper, we compute exactly the average density of a harmonically confined Riesz gas of $N$ particles for large $N$ in the presence of a hard wall. In this Riesz gas, the particles repel each other via a pairwise interaction that behaves as $|x_i - x_j|^{-k}$ for $k>-2$, with $x_i$ denoting the position of the $i^{\rm th}$ particle. This density can be classified into three different regimes of $k$. For $k \geq 1$, where the interactions are effectively short-ranged, the appropriately scaled density has a finite support over $[-l_k(w),w]$ where $w$ is the scaled position of the wall. Whi…

Repulsion of an evolving surface on walls with random heights

We consider the motion of a discrete random surface interacting by exclusion with a random wall. The heights of the wall at the sites of $\Z^d$ are i.i.d.\ random variables. Fixed the wall configuration, the dynamics is given by the serial harness process which is not allowed to go below the wall. We study the effect of the distribution of the wall heights on the repulsion speed.