6,030 research outputs found
Large deviations principle for Curie-Weiss models with random fields
In this article we consider an extension of the classical Curie-Weiss model
in which the global and deterministic external magnetic field is replaced by
local and random external fields which interact with each spin of the system.
We prove a Large Deviations Principle for the so-called {\it magnetization per
spin} with respect to the associated Gibbs measure, where is
the scaled partial sum of spins. In particular, we obtain an explicit
expression for the LDP rate function, which enables an extensive study of the
phase diagram in some examples. It is worth mentioning that the model
considered in this article covers, in particular, both the case of i.\,i.\,d.\
random external fields (also known under the name of random field Curie-Weiss
models) and the case of dependent random external fields generated by e.\,g.\
Markov chains or dynamical systems.Comment: 11 page
A QUALITATIVE ANALYSIS OF THE HIGH RACQUET POSITION BACKHAND DRIVE OF AN ELITE RACQUETBALL PLAYER
Since 1950, when Joe Sobek put strings on his paddleball
paddle, the sport of racquetball has grown to the point where it has
attained international status. Today, racquetball is played in 57
countries. It has been granted representation on the United States
Olympic Committee (USOC) and is under consideration as a future
Olympic sport, possible as early as the 1992 games. In spite of its rapid and international growth, racquetball remains a relatively new sport,on which very little research has been reported
McKean-Vlasov limit for interacting random processes in random media
Item does not contain fulltex
Entropic and gradient flow formulations for nonlinear diffusion
Nonlinear diffusion is considered for
a class of nonlinearities . It is shown that for suitable choices of
, an associated Lyapunov functional can be interpreted as thermodynamics
entropy. This information is used to derive an associated metric, here called
thermodynamic metric. The analysis is confined to nonlinear diffusion
obtainable as hydrodynamic limit of a zero range process. The thermodynamic
setting is linked to a large deviation principle for the underlying zero range
process and the corresponding equation of fluctuating hydrodynamics. For the
latter connections, the thermodynamic metric plays a central role
Lymphocyte Defect in Plasmacytoma-bearing Mice
Multiple myeloma is often associated with humoral immunodepression in both man and mouse. When mice bearing the humorally immunodepressive plasmacytomas TEPC-183 and SPQC-11 were injected with SRBC, the rise of serum haemolysins was significantly less than that of non-tumour-bearing mice. Mice with the plasmacytomas MPC-11 and MOPC-315 have an antibody response similar to normal mice when injected with SRBC. Following immunization, normal mice and those bearing MPC-11 showed a 2- to 3-fold increase in total spleen lymphocytes. Mice bearing TEPC-183 or SPQC-11, the plasmacytomas causing an impaired antibody response, has significant increase in spleen lymphocytes under the same conditions. Mice bearing MOPC-315 had a very high initial count of spleen lymphocytes, which did not further increase upon immune stimulation
A sample-path large deviation principle for dynamic Erdős–Rényi random graphs
We consider a dynamic Erdős–Rényi random graph on n vertices in which each edge switches on at rate λ and switches off at rate μ, independently of other edges. The focus is on the analysis of the evolution of the associated empirical graphon in the limit as n → ∞. Our main result is a large deviation principle (LDP) for the sample path of the empirical graphon observed until a fixed time horizon. The rate is (n2 ), the rate function is a specific action integral on the space of graphon trajectories. We apply the LDP to identify (i) the most likely path that starting from a constant graphon creates a graphon with an atypically large density of d-regular subgraphs, and (ii) the mostly likely path between two given graphons. It turns out that bifurcations may occur in the solutions of associated variational problems
Bad configurations for random walk in random scenery and related subshifts
Article / Letter to editorMathematisch Instituu
Binary data corruption due to a Brownian agent
We introduce a model of binary data corruption induced by a Brownian agent
(active random walker) on a d-dimensional lattice. A continuum formulation
allows the exact calculation of several quantities related to the density of
corrupted bits \rho; for example the mean of \rho, and the density-density
correlation function. Excellent agreement is found with the results from
numerical simulations. We also calculate the probability distribution of \rho
in d=1, which is found to be log-normal, indicating that the system is governed
by extreme fluctuations.Comment: 39 pages, 10 figures, RevTe
Fronts in randomly advected and heterogeneous media and nonuniversality of Burgers turbulence: Theory and numerics
A recently established mathematical equivalence--between weakly perturbed
Huygens fronts (e.g., flames in weak turbulence or geometrical-optics wave
fronts in slightly nonuniform media) and the inviscid limit of
white-noise-driven Burgers turbulence--motivates theoretical and numerical
estimates of Burgers-turbulence properties for specific types of white-in-time
forcing. Existing mathematical relations between Burgers turbulence and the
statistical mechanics of directed polymers, allowing use of the replica method,
are exploited to obtain systematic upper bounds on the Burgers energy density,
corresponding to the ground-state binding energy of the directed polymer and
the speedup of the Huygens front. The results are complementary to previous
studies of both Burgers turbulence and directed polymers, which have focused on
universal scaling properties instead of forcing-dependent parameters. The
upper-bound formula can be heuristically understood in terms of renormalization
of a different kind from that previously used in combustion models, and also
shows that the burning velocity of an idealized turbulent flame does not
diverge with increasing Reynolds number at fixed turbulence intensity, a
conclusion that applies even to strong turbulence. Numerical simulations of the
one-dimensional inviscid Burgers equation using a Lagrangian finite-element
method confirm that the theoretical upper bounds are sharp within about 15% for
various forcing spectra (corresponding to various two-dimensional random
media). These computations provide a new quantitative test of the replica
method. The inferred nonuniversality (spectrum dependence) of the front speedup
is of direct importance for combustion modeling.Comment: 20 pages, 2 figures, REVTeX 4. Moved some details to appendices,
added figure on numerical metho
- …