A probe of the Radion-Higgs mixing in the Randall-Sundrum model at e^+ e^- colliders

In the Randall-Sundrum model, the radion-Higgs mixing is weakly suppressed by the effective electroweak scale. A novel feature of the existence of gravity-scalar mixing would be a sizable three-point vertex among the KK graviton, Higgs and radion. We study this vertex in the process e^+ e^- -> h phi, which is allowed only with a non-zero radion-Higgs mixing. It is shown that the angular distribution is a unique characteristic of the exchange of massive spin-2 gravitons, and the total cross section at the future e^+ e^- collider is big enough to cover a large portion of the parameter space where the LEP/LEP II data cannot constrain.Comment: 14pages, RevTeX, 5 figure

Associated production of a single heavy T-quark in the littlest and simplest little Higgs models

The colored SU(2)-singlet heavy T-quark is one of the most crucial ingredients in little Higgs models, which is introduced to cancel the largest contribution of the SM top quark to the Higgs boson mass at one-loop level. In two representative little Higgs models, the littlest Higgs model and the SU(3) simplest Higgs model, we comprehensively study the single heavy T-quark production at Large Hadron Collider (LHC). After presenting the possibility of relatively light (~500 GeV) T-quark in the simplest little Higgs model, we consider all the relevant processes, the 2->2 process of qb->q'T, the 2->3 process of qg->q'Tb, the s-channel process of q bar(q)'->T bar{b}, and the gluon fusion process of gg->T bar{t}. We found that the 2->3 process can be quite important, as its cross section is about 30% of the 2->2 one and it is dominant in high p_T distributions. The s-channel and the gluon fusion processes also show distinctive features in spite of their suppressed cross sections. In the gluon fusion process of the simplest little Higgs model, for example, the pseudo-scalar contribution is rather dominant over the Higgs contribution for relatively light M_T.Comment: 27 pages, using RevTeX; references adde

Convergence of the all-time supremum of a L\'evy process in the heavy-traffic regime

In this paper we derive a technique of obtaining limit theorems for suprema of L\'evy processes from their random walk counterparts. For each $a>0$, let $\{Y^{(a)}_n:n\ge 1\}$ be a sequence of independent and identically distributed random variables and $\{X^{(a)}_t:t\ge 0\}$ be a L\'evy processes such that $X_1^{(a)}\stackrel{d}{=} Y_1^{(a)}$, $\mathbb E X_1^{(a)}<0$ and $\mathbb E X_1^{(a)}\uparrow0$ as $a\downarrow0$. Let $S^{(a)}_n=\sum_{k=1}^n Y^{(a)}_k$. Then, under some mild assumptions, $\Delta(a)\max_{n\ge 0} S_n^{(a)}\stackrel{d}{\to} R\iff\Delta(a)\sup_{t\ge 0} X^{(a)}_t\stackrel{d}{\to} R$, for some random variable $R$ and some function $\Delta(\cdot)$. We utilize this result to present a number of limit theorems for suprema of L\'evy processes in the heavy-traffic regime

Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization

We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size.Comment: 26 page

On exact time-averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterised by a rate of events, \lambda (t), and a magnitude, \Phi, following an exponential distribution. We tackle the problem by performing exact time-averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.Comment: 21 pages, 5 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen

On the Thermodynamic Limit in Random Resistors Networks

We study a random resistors network model on a euclidean geometry \bt{Z}^d. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty', revised version to appear in Journal of Physics

Expected length of the longest common subsequence for large alphabets

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe