منابع مشابه
On self-attracting random walks
In this survey paper we mainly discuss the results contained in two of our recent articles [2] and [5]. Let {Xt}t≥0 be a continuous-time, symmetric, nearest-neighbour random walk on Zd. For every T > 0 we define the transformed path measure dP̂T = (1/ZT ) exp(HT ) dP, where P is the original one and ZT is the appropriate normalizing constant. The Hamiltonian HT imparts the self-attracting intera...
متن کاملErgodicity of self - attracting motion ∗
We study the asymptotic behaviour of a class of self-attracting motions on R. We prove the decrease of the free energy related to the system and mix it together with stochastic approximation methods. We finally obtain the (limit-quotient) ergodicity of the self-attracting diffusion with a speed of convergence.
متن کاملOn the Linear Fractional Self - Attracting Diffusion 3
In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2 < H < 1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized selfintersection lo...
متن کاملStructural properties of self-attracting walks.
Self-attracting walks (SATW) with attractive interaction u>0 display a swelling-collapse transition at a critical u(c) for dimensions d>or=2, analogous to the Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u(c) (swollen walk), above u(c) (collapsed walk), and at u(c), which can be characterized by the fractal dimensions of the clusters d...
متن کاملSwelling-collapse transition of self-attracting walks
We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence of a transition analogous to the Theta transition of polymers. Above a critical attractive interaction u(c), the walk collapses and the exponents nu and k, characterizing the scaling with time t of the mean square end-to-end distance approximatel...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1998
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/31/16/018