Continuous model for homopolymers

Cranston, M.; Koralov, Leonid; Molchanov, Stanislav; Vainberg, Boris

doi:10.1016/j.jfa.2008.07.019

Cited by 61 publications

(75 citation statements)

References 6 publications

(12 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We point out that this kind of questions have been answered in depth in the case of the standard wetting model, that is formally in the a = 0 case, and that the problem of extending these results to the case where the defects are in a strip has been posed in [16], Chapter 2. Note that a closely related pinning model in continuous time has been considered and resolved in [10]; we stress however that their techniques are very peculiar to the continuous time setup. is an interface separating a dry zone from a wet zone.…”

Section: Definition Of the Modelmentioning

confidence: 99%

The scaling limits of a heavy tailed Markov renewal process

Sohier¹

2013

Ann. Inst. H. Poincaré Probab. Statist.

View full text Add to dashboard Cite

In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the α-stable regenerative set. We then apply these results to the strip wetting model which is a random walk S constrained above a wall and rewarded or penalized when it hits the strip [0, ∞) × [0, a] where a is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality. Résumé.Dans cet article, nous considérons des processus de renouvellement markovien à queues lourdes. Nous montrons que, convenablement renormalisés, ils convergent vers l'ensemble régénératif d'indice α. Nous appliquons ces résultats à un modèle d'accrochage dans une bande. Dans ce modèle, une marche aléatoire S, contrainte à rester au-dessus d'un mur, est récompensée ou pénalisée lorsqu'est atteinte la bande [0, ∞) × [0, a] où a est un réel strictement positif. La convergence que nous établissons permet de caractériser les limites d'échelle de ce modèle au point critique. MSC: 60F77; 60K15; 60K20; 60K05; 82B27 Keywords: Heavy tailed Markov renewals processes; Scaling limits; Fluctuation theory for random walks; Regenerative sets k(x, y) := 1 μ(dy) n≥1 K x,dy (n) = n≥1 k x,y (n)is well defined. 484J. Sohier 2. Then sample J as a Markov chain on E starting from some initial point J 0 = x 0 ∈ E and with transition kernel3. Finally sample the increments (τ i − τ i−1 ) i≥1 as a sequence of independent, but not identically distributed random variables according to the conditional law:Markov renewal processes have been introduced independently by Lévy [18] and Smith [21], and their basic properties have been studied by Pyke [19], Cinlar [9] and Pyke and Schauffele [20] among others. A modern reference is Asmussen [1], VII, 4, which describes some applications related to these processes, in particular in the field of queuing theory. More recently, they have been widely used as a convenient tool to describe phenomena arising in models issued from statistical mechanics, and more particularly in models related to pinning models, such as the periodic wetting model ([8] and the monograph [16], Chapter 3) or the 1 + 1 dimensional field with Laplacian interaction ([4] and [5]).We will show our results in the case where the kernel K satisfies the following assumptions.Assumption 1.1. We make the following assumptions on the kernel K:

show abstract

Section: Definition Of the Modelmentioning

confidence: 99%

The scaling limits of a heavy tailed Markov renewal process

Sohier¹

2013

Ann. Inst. H. Poincaré Probab. Statist.

View full text Add to dashboard Cite

show abstract

“…It is known , in the theory of BRWs the problem on the spectrum of a evolutionary operator of mean particle numbers plays an important role. Resolvent analysis of such operators (Cranston M. et al, 2009) has allowed to investigate BRWs with large deviation . The limit theorems on asymptotic behavior of the Green's function for transition probabilities were established.…”

Section: Ergodic Propertymentioning

confidence: 99%

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

Barbiero

Ferrari

2014

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

“…Simon , Cranston et al , etc., considered the same problem for Brownian motion. They derived an exact asymptotic behavior of

e_{μ} (t, x)

in case that μ is a nonnegative, continuous function with compact support.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, they showed that the asymptotic behavior depends on the dimension d and is at most proportional to t . For

α = 2

, Theorem is equivalent to the result of or .…”

Section: Introductionmentioning

confidence: 99%

Large time asymptotics of Feynman–Kac functionals for symmetric stable processes

Takeda

Wada

2016

Mathematische Nachrichten

View full text Add to dashboard Cite

Let μ be a positive Kato measure on Rd associated with the Green kernel of the transient symmetric α‐stable process, the Markov process with generator (−Δ)α/2 (d>α). Let Atμ be the positive continuous additive functional in the Revuz correspondence with μ. If, in addition, μ is of compact support, we give exact large time asymptotics of the expectation of the Feynman–Kac functional, exp(Atμ).

show abstract

Continuous model for homopolymers

Cited by 61 publications

References 6 publications

The scaling limits of a heavy tailed Markov renewal process

The scaling limits of a heavy tailed Markov renewal process

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

Large time asymptotics of Feynman–Kac functionals for symmetric stable processes

Contact Info

Product

Resources

About