相关论文: Tightness conditions for polymer measures

In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random…

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.

We review recent simulation studies of interfaces between immiscible homopolymer phases. Special emphasis is given to the presentation of efficient simulation techniques and powerful methods of data analysis, such as the analysis of…

We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric…

We study the passage (translocation) of a self-avoiding polymer through a membrane pore in two dimensions. In particular, we numerically measure the probability distribution Q(T) of the translocation time T, and the distribution P(s,t) of…

We consider the statistical mechanics of a random polymer with random walks and disorders in $\mathbb{Z}^d$. The walk collects random disorders along the way and gets nothing if it visits the same site twice. In the continuum and weak…

We consider multidimensional random walks in pyramidal cones (or multidimensional orthants), which are intersections of a finite number of half-spaces. We explore the connection between the existence of (positive) discrete harmonic…

The a.s. existence of a polymer probability in the infinite volume limit is readily obtained under general conditions of weak disorder from standard theory on multiplicative cascades or branching random walk. However, speculations in the…

Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the possibility with a certain probability to form an…

We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our…

We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…

We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles stick together and explain how to associate a probability…

Monte Carlo dynamics of the lattice 48 monomers toy protein is interpreted as a random walk in an abstract (discrete) space of conformations. To test the geometry of this space, we examine the return probability $P(T)$, which is the…

We offer a unified treatment of distinct measures of well-posedness for homogeneous conic systems. To that end, we introduce a distance to infeasibility based entirely on geometric considerations of the elements defining the conic system.…

For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.

A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. This difference leads to striking phenomena when the polymer fluctuates in a nonhomogeneous…

We consider a simple random walk of length $N$, denoted by $(S_{i})_{i\in \{1,...,N\}}$, and we define $(w_i)_{i\geq 1}$ a sequence of centered i.i.d. random variables. For $K\in\N$ we define $((\gamma_i^{-K},...,\gamma_i^K))_{i\geq 1}$ an…

We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our…

In this paper we investigate the conformation statistics of a Gaussian chain embedded in a medium of finite size, in the presence of quenched random obstacles. The similarities and differences between the case of random obstacles and the…

We study here the topology of information on the space of probability measures over Polish spaces that was defined in [1]. We show that under this topology, a convergent sequence of probability measures satisfying a conditional independence…