first passage percolation network flows and electrical resistances we show that the first passage times of first passage percolation on 2 are such that p 0n n decay geometrically as n where may represent any of the four usual first passage time processes the former estimate requires no moment condition on the time coordinates but there exists a geometrically decaying estimate for the latter quantity if and only if the time coordinate distribution has finite moment generating function near the origin here is the time constant and 0 we study the line to line first passage times and describe applications to the maximum network flow through a randomly capacitated subsection of 2 and to the asymptotic behaviour of the electrical resistance of a subsection of 2 when the edges of the subsection are wires in an electrical network with random resistances in the latter case we show for example that if each edge resistance equals 1 or ohms with probabilities p and 1 p respectively then the effective resistance rn across opposite faces of an n by n box satisfies the following a if p 1 2 then p rn 1 as n b if p 1 2 then there exists p such that p p 1 underset raise0 3em hbox smash scriptscriptstyle leqslant mathop lim inf r n limits n to infty underset raise0 3em hbox smash scriptscriptstyle leqslant mathop lim sup r n limits n to infty underset raise0 3em hbox smash scriptscriptstyle leqslant v p 1

competition interfaces and second class particles the one dimensional nearest neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last passage percolation model in z 2 we show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last passage percolation model using technology built up for geodesics in percolation we show that the competition interface converges almost surely to an asymptotic random direction as a consequence we get a new proof for the strong law of large numbers for the second class particle in the rarefaction fan and describe the distribution of the asymptotic angle of the competition interface

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

large deviations for increasing sequences on the plane we prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among poisson points on the plane the rate function for lower tail deviations is derived from a 1977 result of logan and shepp about young diagrams of random permutations for the upper tail we use a coupling with hammersley s particle process and convex analytic techniques along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric hammersley s process

mathematical modeling in photoacoustic imaging of small absorbers this paper is devoted to mathematical modeling in photoacoustic imaging of small absorbers we propose a new method for reconstructing small absorbing regions inside a bounded domain from boundary measurements of the induced acoustic signal we also show the focusing property of the back propagated acoustic signal indeed we provide two different methods for locating a targeted optical absorber from boundary measurements of the induced acoustic signal the first method consists of a multiple signal classification music type algorithm and the second one uses a multifrequency approach we also show results of computational experiments to demonstrate efficiency of the algorithms

duality between coalescence times and exit points in last passage percolation models in this article we prove a duality relation between coalescence times and exit points in last passage percolation models with exponential weights as a consequence we get lower bounds for coalescence times with scaling exponent 3 23 2 and we relate its distribution with variational problems involving the brownian motion process and the airy22 process the proof relies on the relation between busemann functions and the burke property for stationary versions of the last passage percolation model with boundary

the burgers equation with poisson random forcing we consider the burgers equation on the real line with forcing given by poissonian noise with no periodicity assumption under a weak concentration condition on the driving random force we prove existence and uniqueness of a global solution in a certain class we describe its basin of attraction that can also be viewed as the main ergodic component for the model we establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics we also prove the diffusive behavior of the global minimizers on the universal cover in the periodic forcing case

space time stationary solutions for the burgers equation we construct space time stationary solutions of the 1d burgers equation with random forcing in the absence of periodicity or any other compactness assumptions more precisely for the forcing given by a homogeneous poissonian point field in space time we prove that there is a unique global solution with any prescribed average ve locity these global solutions serve as one point random attractors for the infinite dimensional dynamical system associated to solutions to the cauchy problem the probability distribution of the global solutions de fines a stationary distribution for the corresponding markov process we describe a broad class of initial cauchy data for which the distribution of the markov process converges to the above stationary distribution our construction of the global solutions is based on a study of the field of action minimizing curves we prove that for an arbitrary value of the average velocity with probability 1 there exists a unique field of action minimizing curves initiated at all of the poissonian points moreover action minimizing curves corresponding to different starting points merge with each other in finite time

on hopf s formulas for solutions of hamilton jacobi equations soit h r n r on considere l equation de hamilton jacobi u t h du 0 dans r n 1 r n 0 on etudie les proprietes des formules de hopf pour les solutions

coalescence of geodesics in exactly solvable models of last passage percolation coalescence of semi infinite geodesics remains a central question in planar first passage percolation in this paper we study finer properties of the coalescence structure of finite and semi infinite geodesics for exactly solvable models of last passage percolation consider directed last passage percolation on z2 with independent and identically distributed exponential weights on the vertices fix two points v1 0 0 and v2 0 k2 3 for some k 0 and consider the maximal paths 1 and 2 starting at v1 and v2 respectively to the point n n for n k our object of study is the point of coalescence i e the point v 1 2 with smallest v 1 we establish that the distance to coalescence v 1 scales as k by showing the upper tail bound p v 1 rk r c for some c 0 we also consider the problem of coalescence for semi infinite geodesics for the almost surely unique semi infinite geodesics in the direction 1 1 starting from v3 k2 3 k2 3 and v4 k2 3 k2 3 we establish the optimal tail estimate p v 1 rk r 2 3 for the point of coalescence v this answers a question left open by pimentel ann probab 44 5 3187 3206 2016 who proved the corresponding lower bound

limiting shape for directed percolation models we consider directed first passage and last passage percolation on the nonnegative lattice z d d 2 with i i d weights at the vertices under certain moment conditions on the common distribution of the weights the limits g x lim n n 1 t nx exist and are constant a s for x r d where t z is the passage time from the origin to the vertex z z d we show that this shape function g is continuous on r d in particular at the boundaries in two dimensions we give more precise asymptotics for the behavior of g near the boundaries these asymptotics depend on the common weight distribution only through its mean and variance in addition we discuss growth models which are naturally associated to the percolation processes giving a shape theorem and illustrating various possible types of behavior with output from simulations

busemann functions and equilibrium measures in last passage percolation models the interplay between two dimensional percolation growth models and one dimensional particle processes has been a fruitful source of interesting mathematical phenomena in this paper we develop a connection between the construction of busemann functions in the hammersley last passage percolation model with i i d random weights and the existence ergodicity and uniqueness of equilibrium or time invariant measures for the related multi class interacting fluid system as we shall see in the classical hammersley model where each point has weight one this approach brings a new and rather geometrical solution of the longest increasing subsequence problem as well as a central limit theorem for the busemann function

hydrodynamic limit for particle systems with nonconstant speed parameter we establish the hydrodynamic limit for a class of particle systems on d with nonconstant speed parameter assuming that the speed parameter is continuously differentiable in the spatial variable if the particle system is on the one dimensional lattice and totally asymmetric we derive the hydrodynamic equation for continuous speed parameters we obtain nontrivial upper and lower bounds when either the speed parameter is discontinuous or there is a blockage at a fixed site

busemann functions and infinite geodesics in two dimensional first passage percolation we study first passage percolation on mathbb z 2 where the edge weights are given by a translation ergodic distribution addressing questions related to existence and coalescence of infinite geodesics some of these were studied in the late 1990s by c newman and collaborators under strong assumptions on the limiting shape and weight distribution in this paper we develop a framework for working with distributional limits of busemann functions and use it to prove forms of newman s results under minimal assumptions for instance we show a form of coalescence of long finite geodesics in any deterministic direction we also introduce a purely directional condition which replaces newman s global curvature condition and whose assumption we show implies the existence of directional geodesics without this condition we prove existence of infinite geodesics which are directed in sectors last we analyze distributional limits of geodesic graphs proving almost sure coalescence and nonexistence of infinite backward paths this result relates to the conjecture of nonexistence of bigeodesics

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

root mean square decomposition for est based spatial multiplexing systems we consider the transceiver design for multiple input multiple output mimo systems when the channel state information csi is available at the transmitter as well as the receiver first we propose an open loop low complexity mimo spatial multiplexing scheme based on the energy spreading transform est sm the est sm can spatially multiplex multiple data streams and iteratively detect the data streams with almost negligible interstream interference at sufficiently high snr then we propose a closed loop precoding scheme suitable for the est sm called root mean square decomposition rmsd scheme the rmsd precoding scheme combined with the est sm decomposes a mimo channel into multiple subchannels with identical snrs this desired property minimizes bit error rate ber when different bit allocations on different subchannels which cause a significant increase in system complexity are not used we show that when the est sm is used the rmsd scheme is optimal in ber performance and it achieves full diversity simulation results show that the rmsd scheme outperforms other existing techniques such as the geometric mean decomposition gmd scheme jiang ieee trans signal process vol 53 no 10 pp 3791 3803 and the uniform channel decomposition ucd scheme1 jiang ieee trans signal process vol 53 no 11 pp 4283 4294 in ber performance

on the number of infinite geodesics and ground states in disordered systems we study first passage percolation models and their higher dimensional analogs models of surfaces with random weights we prove that under very general conditions the number of lines or in the second case hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to as corollaries we show that in any dimensiond 2 the number of ground states of an ising ferromagnet with random coupling constants equals with probability one 2 or proofs employ simple large deviation estimates and ergodic arguments

layer potential methods for elliptic homogenization problems in this paper we use the method of layer potentials to study l 2 boundary value problems in a bounded lipschitz domain for a family of second order elliptic systems with rapidly oscillating periodic coefficients defining l e div a e 1 x under the assumption that a x is elliptic symmetric periodic and holder continuous we establish the solvability of the l 2 dirichlet regularity and neumann problems for l e u e 0 in with optimal estimates uniform in e 0

sharp estimates for the neumann functions and applications to quantitative photo acoustic imaging in inhomogeneous media we obtain sharp lp and holder estimates for the neumann function of the operator ik on a bounded domain we also obtain quantitative description of its singularity we then apply these estimates to quantitative photo acoustic imaging in inhomogeneous media the problem is to reconstruct the optical absorption coefficient of a diametrically small anomaly from the absorbed energy density

global pointwise estimates for green s matrix of second order elliptic systems abstract we establish global pointwise bounds for the green s matrix for divergence form second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate moreover we prove that such a local boundedness estimate for weak solutions of the system is equivalent to the usual global pointwise bound for the green s matrix in the scalar case such an estimate is a consequence of de giorgi moser nash theory and holds for equations with bounded measurable coefficients in arbitrary domains in the vectorial case one need to impose certain assumptions on the coefficients of the system as well as on domains to obtain such an estimate we present a unified approach valid for both the scalar and vectorial cases and discuss several applications of our result

non equilibrium behaviour of a many particle process density profile and local equilibria one considers a simple exclusion particle jump process on where the underlying one particle motion is a degenerate random walk that moves only to the right one starts with the configuration in which the left halfline is completely occupied and the right one free it is shown that the number of particles at time t between site u t and v t divided by t converges a s to int limits u nu f w dw where f might be called the density profile it is explicitely determined and shown to be an affine function secondly we prove that the distribution of the process looked at by an observer travelling at constant speed u converges weakly to the bernoulli measure with density f u as the time tends to infinity

geodesics and spanning trees for euclidean first passage percolation the metric d q q on the set q of particle locations of a homogeneous poisson process on r d defined as the infimum of i q i q i 1 1 over sequences in q starting with q and ending with q where denotes euclidean distance has nontrivial geodesics when a 1 the cases 1 are the euclidean first passage percolation fpp models introduced earlier by the authors while the geodesics in the case are exactly the paths from the euclidean minimal spanning trees forests of aldous and steele we compare and contrast results and conjectures for these two situations new results for 1 and any d include inequalities on the fluctuation exponents for the metric x 1 2 and for the geodesies 3 4 in strong enough versions to yield conclusions not yet obtained for lattice fpp almost surely every semiinfinite geodesic has an asymptotic direction and every direction has a semiinfinite geodesic from every q for d 2 and 2 further results follow concerning spanning trees of semiinfinite geodesics and related random surfaces

quenched free energy and large deviations for random walks in random potentials we study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps the potential can be unbounded and can depend on a few steps of the walk directed undirected and stretched polymers as well as random walk in random environment are covered the restriction needed is on the moment of the potential in relation to the degree of mixing of the ergodic environment we derive two variational formulas for the limiting quenched free energy and prove a process level quenched large deviation principle ldp for the empirical measure as a corollary we obtain ldps for types of random walks in random environments not covered by earlier results 2012 wiley periodicals inc

busemann functions and the speed of a second class particle in the rarefaction fan in this paper we will show how the results found in probab theory related fields 154 2012 89 125 about the busemann functions in last passage percolation can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan in either the totally asymetric exclusion process or the hammersley interacting particle process the method will be to use the well known last passage percolation description of the exclusion process and of the hammersley process and then the well known connection between second class particles and competition interfaces

geodesics and the competition interface for the corner growth model we study the directed last passage percolation model on the planar integer lattice with nearest neighbor steps and general i i d weights on the vertices outside the class of exactly solvable models in georgiou et al probab theory relat fields 2016 doi 10 1007 s00440 016 0729 x we constructed stationary cocycles and busemann functions for this model using these objects we prove new results on the competition interface on existence uniqueness and coalescence of directional semi infinite geodesics and on nonexistence of doubly infinite geodesics

stationary cocycles and busemann functions for the corner growth model we study the directed last passage percolation model on the planar square lattice with nearest neighbor steps and general i i d weights on the vertices outside of the class of exactly solvable models stationary cocycles are constructed for this percolation model from queueing fixed points these cocycles serve as boundary conditions for stationary last passage percolation solve variational formulas that characterize limit shapes and yield existence of busemann functions in directions where the shape has some regularity in a sequel to this paper the cocycles are used to prove results about semi infinite geodesics and the competition interface

burgers turbulence and random lagrangian systems we consider a spatially periodic inviscid random forced burgers equation in arbitrary dimension and the random time dependent lagrangian system related to it we construct a unique stationary distribution for viscosity solutions of the burgers equation we also show that with probability 1 there exists a unique minimizing trajectory for the random lagrangian system which generates a non trivial ergodic invariant measure for the non random skew product extension of the lagrangian system

the attractiveness of the fixed points of a cdot gi 1 queue we consider an infinite tandem of first come first served queues the service times have unit mean and are independent and identically distributed across queues and customers let i be a stationary and ergodic interarrival sequence with marginals of mean r 1 and suppose it is independent of all service times the process i is said to be a fixed point for the first and hence for each queue if the corresponding interdeparture sequence is distributed as i assuming that such a fixed point exists we show that it is the distributional limit of passing an arbitrary stationary and ergodic interarrival process of mean through the infinite queueing tandem

ratios of partition functions for the log gamma polymer we introduce a random walk in random environment associated to an underlying directed polymer model in 1 1 dimensions this walk is the positive temperature counterpart of the competition in terface of percolation and arises as the limit of quenched polymer measures we prove this limit for the exactly solvable log gamma polymer as a consequence of almost sure limits of ratios of parti tion functions these limits of ratios give the busemann functions of the log gamma polymer and furnish centered cocycles that solve a variational formula for the limiting free energy limits of ratios of point to point and point to line partition functions manifest a duality between tilt and velocity that comes from quenched large deviations under polymer measures in the log gamma case we identify a fam ily of ergodic invariant distributions for the random walk in random environment

existence of hydrodynamics for the totally asymmetric simple k exclusion process in a totally asymmetric simple k exclusion process particles take nearest neighbor steps to the right on the lattice z under the constraint that each site contain at most k particles we prove that such processes satisfy hydrodynamic limits under euler scaling and that the limit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function our technique requires no knowledge of the invariant measures of the process which is essential because the equilibria of asymmetric k exclusion are unknown but we cannot calculate the flux function precisely the proof proceeds via a coupling with a growth model on the two dimensional lattice in addition to the basic k exclusion with constant exponential jump rates we treat the site disordered case where each site has its own jump rate randomly chosen but frozen for all time the hydrodynamic limit under site disorder is new even for the simple exclusion process the case k 1 our proof makes no use of the markov property so at the end of the paper we indicate how to treat the case with arbitrary waiting times

the existence of fixed points for the gi 1 queue a celebrated theorem of burke s asserts that the poisson process is a fixed point for a stable exponential single server queue that is when the arrival process is poisson the equilibrium departure process is poisson of the same rate this paper considers the following question do fixed points exist for queues which dispense i i d services of finite mean but otherwise of arbitrary distribution i e the so called gi 1 fcfs queues we show that if the service time s is nonconstant and satisfies p s u 1 2 du then there is an unbounded set s e s oo such that for each e s there exists a unique ergodic fixed point with mean inter arrival time equal to a we conjecture that in fact s e s

absence of geodesics in first passage percolation on a half plane an h geodesic is a doubly infinite path which locally minimizes the passage time in the i i d first passage percolation model on a half plane h under the assumption that the bond passage times are continuously distributed with a finite mean we prove that with probability 1 h geodesics do not exist as a corollary we show that with probability 1 any geodesic in the analogous model on the whole plane z 2 has to intersect all straight lines with rational slopes

order of the variance in the discrete hammersley process with boundaries we discuss the order of the variance on a lattice analogue of the hammersley process with boundaries for which the environment on each site has independent bernoulli distributed values the last passage time is the maximum number of bernoulli points that can be collected on a piecewise linear path where each segment has strictly positive but finite slope we show that along characteristic directions the order of the variance of the last passage time is of order n 2 3 in the model with boundary these characteristic directions are restricted in a cone starting at the origin and along any direction outside the cone the order of the variance changes to o n in the boundary model and to o 1 for the non boundary model this behaviour is the result of the two flat edges of the shape function

hammersley s interacting particle process and longest increasing subsequences in a famous paper 8 hammersley investigated the lengthl n of the longest increasing subsequence of a randomn permutation implicit in that paper is a certain one dimensional continuous space interacting particle process by studying a hydrodynamical limit for hammersley s process we show by fairly soft arguments that limn 1 2 el n 2 this is a known result but previous proofs 14 11 relied on hard analysis of combinatorial asymptotics

differentiability at the edge of the percolation cone and related results in first passage percolation we study first passage percolation in two dimensions using measures on passage times with b inf supp 0 and mu b p geq vec p c the threshold for oriented percolation we first show that for each such the boundary of the limit shape for is differentiable at the endpoints of flat edges in the so called percolation cone we then conclude that the limit shape must be non polygonal for all of these measures furthermore the associated richardson type growth model admits infinite coexistence and if is not purely atomic the graph of infection has infinitely many ends we go on to show that lower bounds for fluctuations of the passage time given by newman piza extend to these measures we establish a lower bound for the variance of the passage time to distance n of order log n in any direction outside the percolation cone under a condition of finite exponential moments for this result confirms a prediction of newman and piza ann probab 23 977 1005 1995 and zhang ann probab 36 331 362 2008 under the assumption of finite radius of curvature for the limit shape in these directions we obtain a power law lower bound for the variance and an inequality between the exponents and

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

boundary layers on sobolev besov spaces and poisson s equation for the laplacian in lipschitz domains we study inhomogeneous boundary value problems for the laplacian in arbitrary lipschitz domains with data in sobolev besov spaces as such this is a natural continuation of work in jerison and kenig j funct anal 1995 16 219 where the inhomogeneous dirichlet problem is treated via harmonic measure techniques the novelty of our approach resides in the systematic use of boundary integral methods in this regard the key results are establishing the invertibility of the classical layer potential operators on scales of sobolev besov spaces on lipschitz boundaries for optimal ranges of indices applications tolp based helmholtz type decompositions of vector fields in lipschitz domains are also presented

stationary coalescing walks on the lattice we consider translation invariant measures on families of nearest neighbor semi infinite walks on the integer lattice we assume that once walks meet they coalesce in 2d we classify the collective behavior of these walks under mild assumptions they either coalesce almost surely or form bi infinite trajectories bi infinite trajectories form measure preserving dynamical systems have a common asymptotic direction in 2d and possess other nice properties we use our theory to classify the behavior of compatible families of semi infinite geodesics in stationary first and last passage percolation we also partially answer a question raised by c hoffman about the limiting empirical measure of weights seen by geodesics we construct several examples our main example is a standard first passage percolation model where geodesics coalesce almost surely but have no asymptotic direction or average weight

geodesics in two dimensional first passage percolation we consider standard first passage percolation on z 2 geodesics are nearest neighbor paths in z 2 each of whose segments is time minimizing we prove part of the conjecture that doubly infinite geodesics do not exist our main tool is a result of independent interest about the coalescing of semi infinite geodesics