排序方式: 共有37条查询结果,搜索用时 390 毫秒
21.
S. Andres M. T. Barlow J.-D. Deuschel B. M. Hambly 《Probability Theory and Related Fields》2013,156(3-4):535-580
We study a continuous time random walk X in an environment of i.i.d. random conductances ${\mu_{e} \in [0,\infty)}$ in ${\mathbb{Z}^d}$ . We assume that ${\mathbb{P}(\mu_{e} > 0) > p_c}$ , so that the bonds with strictly positive conductances percolate, but make no other assumptions on the law of the μ e . We prove a quenched invariance principle for X, and obtain Green’s functions bounds and an elliptic Harnack inequality. 相似文献
22.
Codina Cotar Jean-Dominique Deuschel Stefan Müller 《Communications in Mathematical Physics》2009,286(1):359-376
We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex
potential. We show using a one-step multiple scale analysis the strict convexity of the surface tension at high temperature.
This is an extension of Funaki and Spohn’s result [8], where the strict convexity of potential was crucial in their proof.
Supported by the DFG-Forschergruppe 718 ‘Analysis and stochastics in complex physical systems’. 相似文献
23.
Jean-Dominique Deuschel Daniel W. Stroock Hans Zessin 《Communications in Mathematical Physics》1991,139(1):83-101
In this article, a large deviation principle (cf. Theorem 1.3) for the empirical distribution functional is applied to prove a rather general version of Boltzmann's principle (cf. Theorem 3.5) for models with shift-invariant, finite range potentials. The final section contains an application of these considerations to the two dimensional Ising model at sub-critical temperature.The first two authors acknowledge support from, respectively, the grants NSF DMS-8802667 and NSF DMS-8913328 & DAAL 03-86-K-0171 相似文献
24.
A series of novel 7-membered cyclic sulfonamides have been synthesised using a solid-phase cyclisation-cleavage RCM strategy. Model solution studies indicated the sulfonamides were suitable substrates for RCM using the Grubbs' catalyst 2. Starting from either 2-carboxyethyl polystyrene (21) or Merrifield resin, various seven-membered sulfonamides were prepared in good to excellent yields at low catalyst loadings (2.5-5 mol%) using a flexible spacer between the polymer and the substrate. In addition, a novel double-armed linker was shown to allow efficient RCM cleavage of sulfonamides with as little as 1 mol% of the ruthenium alkylidene complex 2. 相似文献
25.
We consider a random walk on $\mathbb{Z }^d,\ d\ge 2$ , in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from $x\in \mathbb{Z }^d$ to nearest neighbor $x+e$ is the same as to nearest neighbor $x-e$ . Assuming that the environment is genuinely $d$ -dimensional and balanced we show a quenched invariance principle: for $P$ almost every environment, the diffusively rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend both Lawler’s uniformly elliptic result (Comm Math Phys, 87(1), pp 81–87, 1982/1983) and Guo and Zeitouni’s elliptic result (to appear in PTRF, 2010) to the general (non elliptic) case. Our proof is based on analytic methods and percolation arguments. 相似文献
26.
Jean-Dominique Deuschel Ryoki Fukushima 《Stochastic Processes and their Applications》2019,129(1):102-128
We discuss the quenched tail estimates for the random walk in random scenery. The random walk is the symmetric nearest neighbor walk and the random scenery is assumed to be independent and identically distributed, non-negative, and has a power law tail. We identify the long time asymptotics of the upper deviation probability of the random walk in quenched random scenery, depending on the tail of scenery distribution and the amount of the deviation. The result is in turn applied to the tail estimates for a random walk in random conductance which has a layered structure. 相似文献
27.
Igor Bjelaković Jean-Dominique Deuschel Tyll Krüger Ruedi Seiler Rainer Siegmund-Schultze Arleta Szkoła 《Communications in Mathematical Physics》2008,279(2):559-584
Discrete stationary classical processes as well as quantum lattice states are asymptotically confined to their respective
typical support, the exponential growth rate of which is given by the (maximal ergodic) entropy. In the iid case the distinguishability
of typical supports can be asymptotically specified by means of the relative entropy, according to Sanov’s theorem. We give
an extension to the correlated case, referring to the newly introduced class of HP-states. 相似文献
28.
We consider massless Gaussian fields with covariance related to the Green function of a long range random walk on Êd. These are viewed as Gibbs measures for a linear-quadratic interaction. We establish thermodynamic identities and prove a version of Gibbs' variational principle, showing that translation invariant Gibbs measures are characterized as minimizers of the relative entropy density. We then study the large deviations of the empirical field of a Gibbs measure. We show that a weak large deviation principle holds at the volume order, with rate given by the relative entropy density. 相似文献
29.
Jean-Dominique Deuschel Giambattista Giacomin Dmitry Ioffe 《Probability Theory and Related Fields》2000,117(1):49-111
We consider the massless field with zero boundary conditions outside D
N
≡D∩ (ℤ
d
/N) (N∈ℤ+), D a suitable subset of ℝ
d
, i.e. the continuous spin Gibbs measure ℙ
N
on ℝ
ℤd/N
with Hamiltonian given by H(ϕ) = ∑
x,y:|x−y|=1
V(ϕ(x) −ϕ(y)) and ϕ(x) = 0 for x∈D
N
C
. The interaction V is taken to be strictly convex and with bounded second derivative. This is a standard effective model for a (d + 1)-dimensional interface: ϕ represents the height of the interface over the base D
N
. Due to the choice of scaling of the base, we scale the height with the same factor by setting ξ
N
= ϕ/N.
We study various concentration and relaxation properties of the family of random surfaces {ξ
N
} and of the induced family of gradient fields ∇
N
ξ
N
as the discretization step 1/N tends to zero (N→∞). In particular, we prove a large deviation principle for {ξ
N
} and show that the corresponding rate function is given by ∫
D
σ(∇u(x))dx, where σ is the surface tension of the model. This is a multidimensional version of the sample path large deviation principle.
We use this result to study the concentration properties of ℙ
N
under the volume constraint, i.e. the constraint that (1/N
d
) ∑
x∈DN
ξ
N
(x) stays in a neighborhood of a fixed volume v > 0, and the hard–wall constraint, i.e. ξ
N
(x) ≥ 0 for all x. This is therefore a model for a droplet of volume v lying above a hard wall. We prove that under these constraints the field {ξ
N
of rescaled heights concentrates around the solution of a variational problem involving the surface tension, as it would
be predicted by the phenomenological theory of phase boundaries. Our principal result, however, asserts local relaxation properties
of the gradient field {∇
N
ξ
N
(·)} to the corresponding extremal Gibbs states. Thus, our approach has little in common with traditional large deviation
techniques and is closer in spirit to hydrodynamic limit type of arguments. The proofs have both probabilistic and analytic
aspects. Essential analytic tools are ?
p
estimates for elliptic equations and the theory of Young measures. On the side of probability tools, a central role is played
by the Helffer–Sj?strand [31] PDE representation for continuous spin systems which we rewrite in terms of random walk in random environment and by recent results of T. Funaki and H. Spohn [25] on the structure of gradient fields.
Received: 3 March 1999 / Revised version: 9 August 1999 / Published online: 30 March 2000 相似文献
30.
Jean-Dominique Deuschel Giambattista Giacomin 《Communications in Mathematical Physics》1999,206(2):447-462
We study concentration properties of the lattice free field , i.e. the centered Gaussian field with covariance given by the Green function of the (discrete) Laplacian, when constrained
to be positive in a region of volume O(N
d
) (hard–wall condition). It has been shown in [3] that, as N→∞, the conditioned field is pushed to infinity: more precisely the typical value of the ϕ-variable to leading order is , and the exact value of c was found. It was moreover conjectured that the conditioned field, once this diverging height is subtracted, converges weakly
to the lattice free field. Here we prove this conjecture, along with other explicit bounds, always in the direction of clarifying
the intuitive idea that the free field with hard–wall conditioning merely translates away from the hard wall. We give also a proof, alternative to the one presented in [3], of the lower bound on the probability
that the free field is everywhere positive in a region of volume N
d
.
Received: 26 October 1998 / Accepted: 5 April 1999 相似文献