Krishnamurthi Ravishankar

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The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in R × R. We extend the earlier work of Arratia and of Tóth and Werner by providing a new characterization which is then used to obtain convergence results for the BW distribution, including(More)
Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab. Theory Relat. Fields 111, 375-452] constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work(More)
We consider attractive irreducible conservative particle systems on Z, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling exists and is given by the entropy solution to some scalar conservation law with Lipschitz-continuous flux. Our approach is a(More)
We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on Z starting from an arbitrary initial profile. We generalize earlier works by Seppäläinen (1999) and Andjel et al. (2004). Our constructive approach requires new ideas since the subadditive ergodic theorem (central to previous works) is no longer effective in our(More)
We study the problem of broadcasting in a system where n nodes are placed on a line of length L, independently uniformly distributed. We assume that every node is equipped with a transmitter whose radius of transmission is 1. We further assume that simultaneous broadcasts by neighbouring nodes results in garbled messages. The system is synchronous and time(More)
The present study was undertaken to investigate the diuretic effect of ethanolic seed extracts of Macrotyloma uniflorum and Cucumis melo in Albino rats. Ethanolic extracts of the seeds were administered to experimental rats orally at doses of 200mg/kg and 400mg/kg each p.o. Furosemide (5mg/kg) was used as a standard. The diuretic effects of the extracts(More)
We prove a shape theorem for a growing set of simple random walks on Zd, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, the former becomes active as well.(More)
In this paper we consider the lattice filling curve, defined implicitly by Tóth (1995) and explicitly by Tóth and Werner (1998), which forms the boundary between forward and backward coalescing random walks starting from even and odd space-time sub-lattices of Z respectively. We show that this lattice filling curve converges in the diffusive scaling limit(More)