Current fluctuations for independent random walks in multiple dimensions

Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random walks. Consider a box centered around an observer who starts at the origin and moves with constant velocity $\vec{v}$. To observe interesting fluctuations beyond the translation of initial density fluctuations, we measure the net flux of particles over time into this moving box. We call this the ``box-current" process. We generalize this current process to a distribution valued process. Scaling time by $n$ and space by $\sqrt{n}$ gives current fluctuations of order $n^{d/4}$ where $d$ is the space dimension. The scaling limit of the normalized current process is a distribution valued Gaussian process with given covariance. The limiting current process is equal in distribution to the solution of a given stochastic partial differential equation which is related to the generalized Ornstein-Uhlenbeck process.Comment: 31 pages; accepted for publication in Journal of Theoretical Probabilit

Story of a journey: Rutherford to the Large Hadron Collider and onwards

In this article, I set out arguments why the Large Hadron Collider (LHC) : the machine and the experiments with it, are a watershed for particle physics. I give a historical perspective of the essential link between development of particle accelerators and that in our knowledge of the laws governing interactions among the fundamental particles, showing how this journey has reached destination LHC. I explain how the decisions for the LHC design; the energy and number of particles in the beam, were arrived at. I will end by discussing the LHC physics agenda and the time line in which the particle physicists hope to achieve it.Comment: 30 pages, 6 figures, LaTe

Physics Potential of the Next Generation Colliders

In this article I summarize some aspects of the current status of the field of high energy physics and discuss how the next generation of high energy colliders will aid in furthering our basic understanding of elementary particles and interactions among them, by shedding light on the mechanism for the spontaneous breakdown of the Electroweak Symmetry.Comment: 42 pages, 27 figures, LaTeX, Invited article for the special issue on High Energy Physics of the Indian Journal of Physics on the occasion of its Platinum Jubile

Supersymmetry at the PLC

In this talk I will begin with a very brief discussion as to why TeV scale Supersymmetry forms an important subject of the studies at all the current and future Colliders. Then, I will give different examples where the Photon Linear Collider, PLC, will be able to make unique contributions. PlC's most important role is in the context of Higgs Physics, due to its ability of accurate determination of $\Gamma_{\gamma \gamma}$ as well as the possibilities it offers for the determination of the CP property of the Higgs boson and of possible CP mixing in the Higgs sector. Further, the PLC can provide probes of SUSY in the regions of the SUSY parameter space, which are either difficult or inaccessible at the LHC and also in the $e^+e^-$ mode of the International Linear Collider (ILC).Comment: 14 pages, LaTeX, 8 figures, uses appolb.cls, included in the submission, talk presented at the PLC2005 workshop, Kazimierz Sept. 5-8, 2005, To appear in Acta Physica Polonic

Photon Structure Function

After briefly explaining the idea of photon structure functions (\f2gam\ , \flgam) I review the current theoretical and experimental developements in the subject of extraction of \qvph\ from a study of the Deep Inelastic Scattering (DIS). I then end by pointing out recent progress in getting information about the parton content of the photon from hard processes other than DIS.Comment: 14 pages, 6 postscript figures, latex, uses equation.sty and epsfig.sty .sty files not adde

SUSY and SUSY Breaking Scale at the Linear Collider

After summarising very briefly the key features of different model predictions for sparticle masses and their relation with the supersymmetry (SUSY) breaking scales and parameters, I discuss the capabilities of an $e^+ e^-$ Linear Collider (LC) with $\sqrt{s} \geq$ 500 GeV for precision measurements of sparticle properties. Then I focus on the lessons one can learn about the scale and mechanism of SUSY breaking from these measurements and point out how LC can crucially complement and extend the achievements of the LHC. I end by mentioning what would be the desired extensions in the type/energy of the colliding particles and their luminosity from the point of view of SUSY investigations.Comment: 28 pages, 17 figures, LaTeX, uses aipproc.cls and aipproc.sty. Plenary talk given at the International Linear Collider Workshop (LCWS) 2000, October 26-30, 2000, Fermila