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1.
László Erdős 《Probability Theory and Related Fields》1998,112(3):321-371
We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional
magnetic Schr?dinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is
repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom
of the spectrum. This result complements the earlier (nonrigorous) calculations by Brézin, Gross and Itzykson which predict
that the IDS is discontinuous at the bottom of the spectrum for zero range (Dirac delta) impurities at low density. We also
elucidate the reason behind this apparent controversy. Our methods involve magnetic localization techniques (both in space
and energy) in addition to a modified version of the “enlargement of obstacles” method developed by A.-S. Sznitman.
Received: 20 July 1997 / Revised version: 20 April 1998 相似文献
2.
Christof Külske 《Probability Theory and Related Fields》2001,119(1):1-30
Can the joint measures of quenched disordered lattice spin models (with finite range) on the product of spin-space and disorder-space
be represented as (suitably generalized) Gibbs measures of an “annealed system”? - We prove that there is always a potential
(depending on both spin and disorder variables) that converges absolutely on a set of full measure w.r.t. the joint measure
(“weak Gibbsianness”). This “positive” result is surprising when contrasted with the results of a previous paper [K6], where
we investigated the measure of the set of discontinuity points of the conditional expectations (investigation of “a.s. Gibbsianness”).
In particular we gave natural “negative” examples where this set is even of measure one (including the random field Ising
model). Further we discuss conditions giving the convergence of vacuum potentials and conditions for the decay of the joint
potential in terms of the decay of the disorder average over certain quenched correlations. We apply them to various examples.
From this one typically expects the existence of a potential that decays superpolynomially outside a set of measure zero.
Our proof uses a martingale argument that allows to cut (an infinite-volume analogue of) the quenched free energy into local
pieces, along with generalizations of Kozlov's constructions.
Received: 11 November 1999 / Revised version: 18 April 2000 / Published online: 22 November 2000
RID="*"
ID="*" Work supported by the DFG Schwerpunkt `Wechselwirkende stochastische Systeme hoher Komplexit?t' 相似文献
3.
Paul Seignourel 《Probability Theory and Related Fields》2000,118(3):293-322
We present discrete schemes for processes in random media. We prove two results. The first one is the convergence of Sinai's
random walks in random environments to the Brox model. The second one is the convergence of random walks in media with random
“gates” to a continuous process in a Poisson potential. The proofs are based on the following idea: we consider the discrete
media as random potentials for continuous models.
Received: 6 May 1999 / Revised version: 18 October 1999 / Published online: 20 October 2000 相似文献
4.
An integral test (Theorem 5) is established for the dichotomy concerning local extinction and survival (even persistence)
at late times for critical multitype spatially homogeneous branching particle systems in continuous time. Our conditions on
the branching mechanism are close to the ones known from “classical” processes without motion component. This generalizes
and complements results of López-Mimbela and Wakolbinger [LMW96] and others. Our approach is based on some genealogical tree
analysis combined with the study of the long-term behavior of L
1-norms of solutions of related systems of reaction-“diffusion” equations, which is perhaps also of some independent interest.
Received: 13 August 1997 / Revised version: 12 May 1998 / Published online: 14 February 2000 相似文献
5.
6.
We consider the parabolic Anderson problem ∂
t
u = κΔu + ξ(x)u on ℝ+×ℝ
d
with initial condition u(0,x) = 1. Here κ > 0 is a diffusion constant and ξ is a random homogeneous potential. We concentrate on the two important cases
of a Gaussian potential and a shot noise Poisson potential. Under some mild regularity assumptions, we derive the second-order
term of the almost sure asymptotics of u(t, 0) as t→∞.
Received: 26 July 1999 / Revised version: 6 April 2000 / Published online: 22 November 2000 相似文献
7.
J.-D. Deuschel Y. Velenik<!-ID=""Supported by DFG grant De /-.--> 《Probability Theory and Related Fields》2000,116(3):359-377
We consider a model of a two-dimensional interface of the (continuous) SOS type, with finite-range, strictly convex interactions.
We prove that, under an arbitrarily weak pinning potential, the interface is localized. We consider the cases of both square
well and δ potentials. Our results extend and generalize previous results for the case of nearest-neighbours Gaussian interactions
in [7] and [11]. We also obtain the tail behaviour of the height distribution, which is not Gaussian.
Received: 3 November 1998 / Revised version: 14 June 1999 相似文献
8.
Anton Bovier Michael Eckhoff Véronique Gayrard Markus Klein 《Probability Theory and Related Fields》2001,119(1):99-161
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field
models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem
to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the Wentzell-Freidlin
theory in this case, showing that any transition can be decomposed, with probability exponentially close to one, into a deterministic
sequence of “admissible transitions”. For these admissible transitions we give upper and lower bounds on the expected transition
times that differ only by a constant factor. The distributions of the rescaled transition times are shown to converge to the
exponential distribution. We exemplify our results in the context of the random field Curie-Weiss model.
Received: 26 November 1998 / Revised version: 21 March 2000 / Published online: 14 December 2000 相似文献
9.
Michel Talagrand 《Probability Theory and Related Fields》2000,117(4):449-466
In the previous paper in this volume we have studied the p-spin interaction model just below the critical temperature, and we have rigorously proved several aspects of the physicists
prediction that this model exhibits “one level of symmetry breaking”. In the present paper we show how to construct systems
that exhibit an arbitrarily large, but finite number of “levels of symmetry-breaking”. As the temperature decreases, such
systems exhibit many phase transitions, as the structure of the overlaps gains complexity. This phenomenon does not seem to
have been described previously, even in the physics literature.
Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000 相似文献
10.
A. de Acosta 《Probability Theory and Related Fields》2000,118(4):483-521
We prove an abstract large deviation result for a sequence of random elements of a vector space satisfying an “abstract exponential
martingale condition”. The framework naturally generates non-convex rate functions. We apply the result to solutions of It?
stochastic equations in R
d
driven by Brownian motion and a Poisson random measure.
Received: 23 June 1999 / Revised version: 17 February 2000 / Published online: 22 November 2000 相似文献
11.
The long-time dynamical properties of solutions (φ,A) to the time-dependent Ginzburg–Landau (TDGL) equations of superconductivity are investigated. The applied magnetic field
varies with time, but it is assumed to approach a long-time asymptotic limit. Sufficient conditions (in terms of the time
rate of change of the applied magnetic field) are given which guarantee that the dynamical process defined by the TDGL equations
is asymptotically autonomous, i.e., it approaches a dynamical system as time goes to infinity. Analyticity of an energy functional
is used to show that every solution of the TDGL equations asymptotically approaches a (single) stationary solution of the
(time-independent) Ginzburg–Landau equations. The standard “φ = − ∇ · A” gauge is chosen.
(Received 30 June 2000; in revised form 30 December 2000) 相似文献
12.
Yu. A. Volkov 《Theoretical and Mathematical Physics》2007,151(1):556-565
We show that the method of “finite-size” particles is a discrete model of the Vlasov equation but in a different (effective)
interaction potential. We calculate the effective potential explicitly in the most interesting case of the Coulomb interaction.
We find the equations of motion of particles of “finite size” for the Gaussian form factor.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 138–148, April, 2007. 相似文献
13.
The interaction of two charges moving in ℝ3 in a magnetic field B can be formulated as a Hamiltonian system with six degrees of freedom. Assuming that the magnetic field is uniform and the
interaction potential has rotation symmetry, we reduce this system to one with three degrees of freedom. For special values
of the conserved quantities, choices of parameters or restriction to the coplanar case, we obtain systems with two degrees
of freedom. Specialising to the case of Coulomb interaction, these reductions enable us to obtain many qualitative features
of the dynamics. For charges of the same sign, the gyrohelices either “bounce-back”, “pass-through”, or exceptionally converge
to coplanar solutions. For charges of opposite signs, we decompose the state space into “free” and “trapped” parts with transitions
only when the particles are coplanar. A scattering map is defined for those trajectories that come from and go to infinite
separation along the field direction. It determines the asymptotic parallel velocities, guiding centre field lines, magnetic
moments and gyrophases for large positive time from those for large negative time. In regimes where gyrophase averaging is
appropriate, the scattering map has a simple form, conserving the magnetic moments and parallel kinetic energies (in a frame
moving along the field with the centre of mass) and rotating or translating the guiding centre field lines. When the gyrofrequencies
are in low-order resonance, however, gyrophase averaging is not justified and transfer of perpendicular kinetic energy is
shown to occur. In the extreme case of equal gyrofrequencies, an additional integral helps us to analyse further and prove
that there is typically also transfer between perpendicular and parallel kinetic energy.
相似文献
14.
Rainer Buckdahn Marc Quincampoix Aurel Răşcanu 《Probability Theory and Related Fields》2000,116(4):485-504
In the present paper, we study conditions under which the solutions of a backward stochastic differential equation remains
in a given set of constraints. This property is the so-called “viability property”. In a separate section, this condition
is translated to a class of partial differential equations.
Received: 23 April 1998 / Published online: 14 February 2000 相似文献
15.
We construct an asymptotics of the solution the Laplace equation in a “long” rectangle with the directional derivative given
on its “long sides” and Dirichlet data on its “short sides.” By using the asymptotics, we calculate one of the integral characteristics,
namely, the magnetoresistance. We obtain new formulas for the low-magnetic field magnetoresistance.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 520–532, April, 1999. 相似文献
16.
We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with
equal spin-spin coupling constants. We show that in the case of “easy axis” anisotropy, the line has a logarithmic low-frequency
singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of
heat capacity. In the case of “easy plane” anisotropy, the line has the traditional Gaussian form. We discuss the possibility
of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system. 相似文献
17.
Yu. Baryshnikov 《Probability Theory and Related Fields》2001,119(2):256-274
Consider the process D
k
, k = 1,2,…, given by
B
i
being independent standard Brownian motions. This process describes the limiting behavior “near the edge” in queues in series,
totally asymmetric exclusion processes or oriented percolation. The problem of finding the distribution of D. was posed in [GW]. The main result of this paper is that the process D. has the law of the process of the largest eigenvalues of the main minors of an infinite random matrix drawn from Gaussian
Unitary Ensemble.
Received: 17 November 1999 / Revised version: 4 April 2000 / Published online: 24 January 2000 相似文献
18.
Michel Talagrand 《Probability Theory and Related Fields》2000,117(3):303-360
We prove that, just below the critical temperature, the mean field p-spins interaction model, for p suitably large, spontaneously decomposes into different states. The asymptotic overlaps between any two different states
are zero. Under a mild (unproven) hypothesis on the weight distribution of these states, we prove that they are pure states.
This situation is called in physics “one level of symmetry breaking”.
Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000 相似文献
19.
S. M. Anan'evskii 《Journal of Mathematical Sciences》1999,93(3):259-264
A modified “parking” problem is considered. Segments of different length fill a large interval (in our case, there are two
kinds of segments). The asymptotics of the mean number of segmentsplaced are obtained. Bibliography: 2 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 16–23. 相似文献
20.
Hilbert–Kunz multiplicity is known to be a very mysterious invariant of a ring or an ideal. We will show a very beautiful
formula on Hilbert–Kunz multiplicity for integrally closed ideals in two-dimensional Gorenstein rational singularities. In
the proof, “McKay correspondence” and “Riemann–Roch formula” play essential roles. Also this formula gives a new significance
to “good ideals”.
Received: 25 October 2000 相似文献