共查询到20条相似文献,搜索用时 31 毫秒
1.
We define a class of weakly self-avoiding walks on the integers by conditioning a simple random walk of length n to have a p-fold self-intersection local time smaller than n
β
, where 1<β<(p+1)/2. We show that the conditioned paths grow of order n
α
, where α=(p−β)/(p−1), and also prove a coarse large deviation principle for the order of growth. 相似文献
2.
Irmina Herburt 《Mathematical Physics, Analysis and Geometry》2007,10(3):251-259
The dual volume of order α of a convex body A in R
n
is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R3 coincides with the maximizer of dual volume of order 2, thus it is unique.
相似文献
3.
Charles Bordenave Pietro Caputo Djalil Chafa? 《Communications in Mathematical Physics》2011,307(2):513-560
Let (X
jk
)
j,k ≥ 1 be i.i.d. complex random variables such that |X
jk
| is in the domain of attraction of an α-stable law, with 0 < α < 2. Our main result is a heavy tailed counterpart of Girko’s circular law. Namely, under some additional smoothness assumptions
on the law of X
jk
, we prove that there exist a deterministic sequence a
n
~ n
1/α
and a probability measure μ
α
on
\mathbbC{\mathbb{C}} depending only on α such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix (an-1Xjk)1 £ j,k £ n{(a_n^{-1}X_{jk})_{1\leq j,k\leq n}} converges weakly to μ
α
as n → ∞. Our approach combines Aldous & Steele’s objective method with Girko’s Hermitization using logarithmic potentials. The
underlying limiting object is defined on a bipartized version of Aldous’ Poisson Weighted Infinite Tree. Recursive relations
on the tree provide some properties of μ
α
. In contrast with the Hermitian case, we find that μ
α
is not heavy tailed. 相似文献
4.
Alessandra Iacobucci Frédéric Legoll Stefano Olla Gabriel Stoltz 《Journal of statistical physics》2010,140(2):336-348
We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy
and momentum. The strength of the stochastic noise is controlled by a parameter γ. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to κ(n)∼n
α
, with 0<α≤1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent α of the divergence depends on γ. 相似文献
5.
Bernard Derrida Giambattista Giacomin Hubert Lacoin Fabio Lucio Toninelli 《Communications in Mathematical Physics》2009,287(3):867-887
We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(·) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K(n) = n
−α-1
L(n), with α ≥ 0 and L(·) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in
the delocalized phase and positive in the localized phase. For α < 1/2 disorder is irrelevant: quenched and annealed critical points coincide for small disorder, as well as quenched and
annealed critical exponents [3,28]. The same has been proven also for α = 1/2, but under the assumption that L(·) diverges sufficiently fast at infinity, a hypothesis that is not satisfied in the (1 + 1)-dimensional wetting model considered
in [12,17], where L(·) is asymptotically constant. Here we prove that, if 1/2 < α < 1 or α > 1, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their
difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case.
In the marginal case α = 1/2, under the assumption that L(·) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which
is smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered in [12,17] is out of our analysis and remains open.
The results are achieved by setting the parameters of the model so that the annealed system is localized, but close to criticality,
and by first considering a quenched system of size that does not exceed the correlation length of the annealed model. In such
a regime we can show that the expectation of the partition function raised to a suitably chosen power is small. We then exploit such an information to prove that the expectation of the same fractional power of the partition
function goes to zero with the size of the system, a fact that immediately entails that the quenched system is delocalized. 相似文献
6.
We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference
in the efficiency in these two cases. The average time to generate an independent sample of configuration of polymer with
n monomers varies as n
2 for linear polymers for large n, but as exp(cn
α) for branched (undirected and directed) polymers, where 0<α<1. On the binary tree, our numerical studies for n of order 104 gives α = 0.333±0.005. We argue that α =1/3 exactly in this case.
An erratum to this article can be found at . 相似文献
7.
A new method is proposed for setting a lower or upper limit a α
n
* on the neutron electric polarizability α
an
. It is based on the fact that the real part of the s-wave scattering amplitude changes sign near the s-wave neutron resonance at E=E*. The methods consist of the observation of the energy behavior of the forward-backward scattering asymmetry ω
1 which experiences a jump at E=E*. If the jump is such that dω
1/dE>0, then α
n
>α
n
*, while if dω
1/dE<0, then α
n
<α
n
*, and if dω
1/dE∼0, then α
n
∼α
n
*. Seven even-even nuclei are found with α
n
* from 0.5 to 3.1 in 10−3 fm3. Some details of a possible experiment with 182W are described.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 171–174 (10 August 1999)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
8.
In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett.
94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where n ≤ L and L is the length of the polymer chain. The RNA structures found in the model can be separated into two regimes: (i) 0 ≤ α ≤ 1, n < L and 0 ≤ α < 1, n = L where unpaired and paired base structures exist and (ii) α = 1, n = L with only completely paired base structures. Figures for the genus distribution functions show differences at small lengths.
We consider the situation when the strength of external perturbation is different on different bases in the polymer chain. 相似文献
9.
Fabio Lucio Toninelli 《Communications in Mathematical Physics》2008,280(2):389-401
We consider a renewal process τ = {τ
0, τ
1,...} on the integers, where the law of τ
i
− τ
i-1 has a power-like tail P(τ
i
− τ
i-1 = n) = n
−(α+1)
L(n) with α ≥ 0 and L(·) slowly varying. We then assign a random, n-dependent reward/penalty to the occurrence of the event that the site n belongs to τ. In such generality this class of problems includes, among others, (1 + d)-dimensional models of pinning of directed polymers on a one-dimensional random defect, (1 + 1)-dimensional models of wetting
of disordered substrates, and the Poland-Scheraga model of DNA denaturation. By varying the average of the reward, the system
undergoes a transition from a localized phase, where τ occupies a finite fraction of to a delocalized phase, where the density of τ vanishes. In absence of disorder (i.e., if the reward is independent of n), the transition is of first order for α > 1 and of higher order for α < 1. Moreover, for α ranging from 1 to 0, the transition ranges from first to infinite order. Presence of even an arbitrarily
small (but extensive) amount of disorder is known to modify the order of transition as soon as α > 1/2 [11]. In physical terms, disorder is relevant in this situation, in agreement with the heuristic Harris criterion.
On the other hand, for 0 < α < 1/2 it has been proven recently by K. Alexander [2] that, if disorder is sufficiently weak, critical exponents are not
modified by randomness: disorder is irrelevant. In this work, generalizing techniques which in the framework of spin glasses
are known as replica coupling and interpolation, we give a new, simpler proof of the main results of [2]. Moreover, we (partially) justify a small-disorder expansion worked
out in [9] for α < 1/2, showing that it provides a free energy upper bound which improves the annealed one. 相似文献
10.
Parking on a Random Tree 总被引:1,自引:1,他引:0
Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating
function G(s). We consider the following variation of Rényi’s parking problem, alternatively called blocking RSA (random sequential adsorption):
at every vertex of the tree a particle (or “car”) arrives with rate one. The particle sticks to the vertex whenever the vertex
and all of its nearest neighbors are not occupied yet.
We provide an explicit expression for the so-called parking constant in terms of the generating function. That is, the occupation
probability, averaged over dynamics and the probability distribution of the random trees converges in the large-time limit
to (1−α
2)/2 with
. 相似文献
11.
Juraj Kumičák 《Czechoslovak Journal of Physics》1999,49(4):527-537
A model of 1/f noise is considered, based on moving averages of ordern. The coefficientsα
k
defining the model are calculated numerically using Seidel iteration which turns out to converge rapidly. The convergence
is independent ofn which seems to be caused by the fact that the nonlinear problem solved is defined by a self-similar matrix. The coefficientsα
k
appear to approach, with indefinitely growingn, valuesα
k
=1/√k and thus the model has a kind of Fourier invariance. Physical interpretation of the invariance is suggested as well
as of coefficientsα
k
describing long-range correlations. Fractal sets of dimensiond=2.5 are proposed to play certain role in explaining the latter.
This work was partly supported by the Scientific Grant Agency of the Ministry of Education of Slovak Republic (VEGA) under
the Grant No. 1/3143/96 and by the Slovak Literary Fund. 相似文献
12.
Consider a family of infinite tri-diagonal matrices of the form L + zB, where the matrix L is diagonal with entries L
kk
= k
2, and the matrix B is off-diagonal, with nonzero entries B
k,k+1 = B
k+1,k
= k
α
, 0 ≤ α < 2. The spectrum of L + zB is discrete. For small |z| the nth eigenvalue E
n
(z), E
n
(0) = n
2, is a well-defined analytic function. Let R
n
be the convergence radius of its Taylor’s series about z = 0. It is proved that
Rn £ C(a) n2-a \textif\enspace 0 £ a < 11 /6R_n \leq C(\alpha) n^{2-\alpha}\quad \text{if}\enspace 0 \leq \alpha <11 /6 相似文献
13.
A novel two-wavelength mid-infrared laser-absorption diagnostic has been developed for simultaneous measurements of vapor-phase
fuel mole fraction and liquid fuel film thickness. The diagnostic was demonstrated for time-resolved measurements of n-dodecane liquid films in the absence and presence of n-decane vapor at 25°C and 1 atm. Laser wavelengths were selected from FTIR measurements of the C–H stretching band of vapor
n-decane and liquid n-dodecane near 3.4 μm (3000 cm−1). n-Dodecane film thicknesses <20 μm were accurately measured in the absence of vapor, and simultaneous measurements of n-dodecane liquid film thickness and n-decane vapor mole fraction (300 ppm) were measured with <10% uncertainty for film thicknesses <10 μm. A potential application
of the measurement technique is to provide accurate values of vapor mole fraction in combustion environments where strong
absorption by liquid fuel or oil films on windows make conventional direct absorption measurements of the gas problematic. 相似文献
14.
We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at least θ occupied neighbors, occupied sites remain occupied forever. It is known that, when b>θ≥2, the limiting density q=q(p) of occupied sites exhibits a jump at some p
T=p
T(b,θ)∈(0,1) from q
T:=q(p
T)<1 to q(p)=1 when p>p
T. We investigate the metastable behavior associated with this transition. Explicitly, we pick p=p
T+h with h>0 and show that, as h
↓0, the system lingers around the “critical” state for time order h
−1/2 and then passes to fully occupied state in time O(1). The law of the entire configuration observed when the occupation density is q∈(q
T,1) converges, as h
↓0, to a well-defined measure. 相似文献
15.
We present a maximum-entropy model for the transport of waves through a classically chaotic cavity in the presence of absorption.
The entropy of the S-matrix statistical distribution is maximized, with the constraint 〈TrSS
†〉 = αn: n is the dimensionality of S, and 0 ≤ α ≤ 1. For α = 1 the S-matrix distribution concentrates on the unitarity sphere and we have no absorption; for α = 0 the distribution becomes a delta function at the origin and we have complete absorption. For strong absorption our result
agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual
(angular) transmission and reflection coefficients becomes exponential — Rayleigh statistics — even for n = 1. For n ≫ 1 Rayleigh statistics is attained even with no absorption; here we extend the study to α<1. The model is compared with random-matrixtheory numerical simulations: it describes the problem very well for strong absorption,
but fails for moderate and weak absorptions. The success of the model for strong absorption is understood in the light of
a central-limit theorem. For weak absorption, some important physical constraint is missing in the construction of the model. 相似文献
16.
Osamu Yamashita Hirotaka Odahara Takahiro Ochi Kouji Satou 《Applied Physics A: Materials Science & Processing》2009,94(1):57-64
The resultant local Seebeck coefficient α
R (=α
S−α
T) at the interface of a thermoelement has not yet been measured, although it is an important factor governing the thermoelectric
efficiency, where α
S is the local Seebeck coefficient and α
T is the one caused by the Thomson effect. It is shown in this paper that α
S, α
T, and α
R of the p- and n-type Cu/Bi–Te/Cu composites are obtained analytically and experimentally on the assumption that the local temperature of
the composite on which the temperature difference ΔT is imposed varies linearly with changes in position along the composite. They were indeed estimated as a function of position
from the local experimental data of R,ΔI,ΔT, and V generated by applying an additional current of ±I to the composite, where R is the electrical resistance and ΔI is a current generated by the composite. As a result, it was found that the absolute values of α
S at the hot interface of the p- and n-type composites are approximately 1.5 and 1.4 times higher than their lowest values in the middle region of the composite,
respectively, while those of α
T are less than 8% of α
S all over the composite and are so small that the relation α
R≈α
S can be held. We thus succeeded in measuring α
R at the interfaces of the composite. 相似文献
17.
We introduce a family of real random polynomials of degree n whose coefficients a
k
are symmetric independent Gaussian variables with variance
, indexed by a real α≥0. We compute exactly the mean number of real roots 〈N
n
〉 for large n. As α is varied, one finds three different phases. First, for 0≤α<1, one finds that
. For 1<α<2, there is an intermediate phase where 〈N
n
〉 grows algebraically with a continuously varying exponent,
. And finally for α>2, one finds a third phase where 〈N
n
〉∼n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for
large n, a finite fraction of their roots 〈N
n
〉/n are real. This condensation occurs via a localization of the real roots around the values
, 1≪k≤n. 相似文献
18.
Wen-Xin Qin 《Communications in Mathematical Physics》2012,311(2):513-538
In this paper we are mainly concerned with existence and modulation of uniform sliding states for particle chains with damping
γ and external driving force F. If the on-site potential vanishes, then for each F > 0 there exist trivial uniform sliding states x
n
(t) = n
ω + ν
t + α for which the particles are uniformly spaced with spacing ω > 0, the sliding velocity of each particle is ν = F/γ, and the phase α is arbitrary. If the particle chain with convex interaction potential is placed in a periodic on-site potential,
we show under some conditions the existence of modulated uniform sliding states of the form
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