Ballistic Phase of Self-Interacting Random Walks

Ioffe, Dmitry; Velenik, Yvan

doi:10.1093/acprof:oso/9780199239252.003.0003

Cited by 37 publications

(115 citation statements)

References 11 publications

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“…In its turn, S + t is a diffusion semigroup with transition kernel 16) which is self-adjoint on L 2 (A + n , ∆ 2 ); the generator of the corresponding ergodic diffusion on A + n is given by…”

Section: )mentioning

confidence: 99%

Dyson Ferrari–Spohn diffusions and ordered walks under area tilts

Ioffe

Velenik

Wachtel

2017

Probab. Theory Relat. Fields

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Abstract. We consider families of non-colliding random walks above a hard wall, which are subject to a self-potential of tilted area type. We view such ensembles as effective models for the level lines of a class of 2 + 1-dimensional discrete-height random surfaces in statistical mechanics. We prove that, under rather general assumptions on the step distribution and on the self-potential, such walks converge, under appropriate rescaling, to non-intersecting Ferrari-Spohn diffusions associated with limiting Sturm-Liouville operators. In particular, the limiting invariant measures are given by the squares of the corresponding Slater determinants.

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Section: )mentioning

confidence: 99%

Dyson Ferrari–Spohn diffusions and ordered walks under area tilts

Ioffe

Velenik

Wachtel

2017

Probab. Theory Relat. Fields

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“…The situation can be adapted to model the adsorption of linear polymers at an impenetrable surface [5,10,15,23] and the general features of the adsorption behaviour are now quite well understood. With the invention of micro-manipulation techniques such as atomic force microscopy (AFM) and optical tweezers that allow individual polymer molecules to be pulled [7,26] there has been renewed interest in how polymers respond to a force and, specifically, how self-avoiding walk models of polymers respond to a force [1,2,8,9,14,17]. There has also been some work on how lattice polygons (a model of ring polymers) respond to a force [2,12,13].…”

Section: Introductionmentioning

confidence: 99%

Self-avoiding walks adsorbed at a surface and pulled at their mid-point

Rensburg¹,

Whittington²

2017

J. Phys. A: Math. Theor.

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Abstract. We consider a self-avoiding walk on the d-dimensional hypercubic lattice, terminally attached to an impenetrable hyperplane at which it can adsorb. When a force is applied the walk can be pulled off the surface and we consider the situation where the force is applied at the middle vertex of the walk. We show that the temperature dependence of the critical force required for desorption differs from the corresponding value when the force is applied at the end-point of the walk. This is of interest in single molecule pulling experiments since it shows that the required force can depend on where the force is applied. We also briefly consider the situation when the force is applied at other interior vertices of the walk.

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“…There are two competing contributions to A h n : Because of the attractive nature of Φ paths prefer to collapse, whereas the drift h pulls them away. The following is known [2,1]: Whichever h one chooses, the mean displacement X(γ)/n satisfies a large deviation principle under A …”

Section: Class Of Models and Resultsmentioning

confidence: 99%