Related papers: Dirichlet forms and polymer models based on stable…
We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$…
In this paper we extend the result obtained in \cite{AKR97} (see also \cite {AKR96}) on the representation of the intrinsic pre- Dirichlet form $\mathcal{E}_{\pi_{\sigma}}^{\Gamma}$ of the Poisson measure $\pi_{\sigma}$ in terms of the…
We study a quenched charged-polymer model, introduced by Garel and Orland in 1988, that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the…
The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a…
In this paper, we consider symmetric $\alpha$-stable processes on (unbounded) horn-shaped regions which are non-uniformly $C^{1,1}$ near infinity. By using probabilistic approaches extensively, we establish two-sided Dirichlet heat…
We investigate the flat phase of $D$-dimensional crystalline membranes embedded in a $d$-dimensional space and submitted to both metric and curvature quenched disorders using a nonperturbative renormalization group approach. We identify a…
In earlier work we provided the first evidence that the collapse, or coil-globule, transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical…
We have mapped the physics of polymer melts onto a time-dependent Landau-Ginzburg $|\psi|^4$ field theory using techniques of functional integration. Time in the theory is simply a label for the location of a given monomer along the extent…
We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking…
In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant and nonlinear…
We introduce and analyze a broad class of continuous directed polymers in $\mathbb{R}^d$ driven by Gaussian environments that are white in time and spatially correlated, under Dalang's condition. Using an It\^o-renormalized…
Recently it has been shown that a two-dimensional model of self-attracting polymers based on attracting segments displays two phase transitions, a theta-like collapse between swollen polymers and a globular state and another between the…
The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an…
We explore the nature of glass-formation in variable spatial dimensionality ($d$) based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an…
Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class…
In this paper we study the unfolding transition observed in polymer stretching experiments. We use a known model and extend it with a mean-field-like interaction. Expressions for all necessary thermodynamic variables as a function of the…
We show that any $\mathbb{R}^d\setminus\{0\}$-valued self-similar Markov process $X$, with index $\alpha>0$ can be represented as a path transformation of some Markov additive process (MAP) $(\theta,\xi)$ in $S_{d-1}\times\mathbb{R}$. This…
We present Molecular Dynamics simulations of the thermal glass transition in a dense model polymer liquid. We performed a comparative study of both constant volume and constant pressure cooling of the polymer melt. Great emphasis was laid…