atmospheres of polygons and knotted polygons in this paper we define two statistics a and a the positive and negative atmospheres of a lattice polygon of fixed length n these statistics have the property that a a pn 2 pn where pn is the number of polygons of length n counted modulo translations we use the pivot algorithm to sample polygons and to compute the corresponding average atmospheres using these data we directly estimate the growth constants of polygons in two and three dimensions we find that where the error bars are 67 confidence intervals and the second error bar in the three dimensional estimate of is an estimated systematic error we also compute atmospheres of polygons of fixed knot type k sampled by the bfacf algorithm we discuss the implications of our results and show that different knot types have atmospheres which behave dramatically differently at small values of n

spherical unitary highest weight representations in this paper we give an almost complete classification of the h spherical unitary highest weight representations of a hermitian lie group g where g h is a symmetric space of cayley type

exact enumeration study of free energies of interacting polygons and walks in two dimensions we present analyses of substantially extended series for both interacting self avoiding walks isaw and polygons isap on the square lattice we argue that these provide good evidence that the free energies of both linear and ring polymers are equal above the temperature thus extending the application of a theorem of tesi et al to two dimensions below the temperature the conditions of this theorem break down in contradistinction to three dimensions but an analysis of the ratio of the partition functions for isap and isaw indicates that the free energies are in fact equal at all temperatures within at least any perceived difference can be interpreted as the difference in the size of corrections to scaling in both problems this may be used to explain the vastly different values of the crossover exponent previously estimated for isap to that predicted theoretically and numerically confirmed for isaw an analysis of newly extended neighbour avoiding self avoiding walk series is also given

the scaling limit of self avoiding random walk in high dimensions the brydges spencer lace expansion is used to prove that the scaling limit of the finite dimensional distributions of self avoiding random walk in the d dimensional cubic lattice mathbb z d is gaussian if d is sufficiently large it is also shown that the critical exponent gamma for the number of self avoiding walks is equal to 1 if d is sufficiently large

on the total number of distinct self interacting self avoiding walks on three dimensional fractal structures we have studied self interacting self avoiding walks saws situated on three dimensional fractal structures represented by a 3d sierpinski gasket sg family of fractals to this end we have applied the exact renormalization group method for the first three members of the sg fractal family b 2 3 and 4 to calculate the critical exponents e and g associated with the total number of distinct saws in extended phase chain and globular collapsed polymer phase respectively to extend the obtained sequence of exact values for e we have applied the monte carlo renormalization group method for fractals with 2 b 40 our results demonstrate that the critical exponent e as a function of b monotonically increases and is always larger than the corresponding three dimensional euclidean value on the other hand for the values b 2 3 and 4 being smaller than the corresponding euclidean value decreases with b

a note on an alternative outlier model summary this paper examines modelling a single outlier in the normal theory fixed effects linear model as arising from an unknown observation with inflated variance the maximum likelihood estimates are characterized in terms of standard least squares statistics the estimated position of the outlier does not necessarily agree with the estimated position under the usual mean slippage outlier model and an example where they differ is presented a sufficient and common condition for agreement is given leads to considering the studentized residuals since under normality and the possibility of each observation being the outlier the maximum likelihood estimate for the position of the possible outlier corresponds to the case with the largest absolute studentized residual also the likelihood ratio test statistic for the presence of an outlier in this model is a monotonic function of the largest absolute studentized residual srikantan 1961 tietjen et al 1973 ellenberg 1976 intuitively one might expect similar results to be true whenever the effect of a single outlier is modelled identically for all observations regardless of values of the independent variables or fixed effects we shall see that this is not necessarily so we consider here a single outlier model that assumes an outlier arises from an error term with an inflated variance box and tiao 1968 consider this model from a bayesian point of view in section 2 the model is defined and shown to be after a parameter transformation a special case of harville s general linear model harville 1977 the joint maximum likelihood estimates mle s are characterized in section 3 and an example where the estimated outlier does not correspond to the observation with the largest absolute studentized residual is presented in section 4 in the final section several issues pertinent to the modelling of outliers are discussed in terms of this model and the mean slippage model our intent here is not to propose this model as a common replacement for the mean slippage model but rather to examine the performance of the mean slippage model under a plausible alternative

on hardy and bergman spaces on complex ol shanskii semigroups let g denote a finite dimensional real lie algebra we call an element x g elliptic if ad x operates semisimply with purely imaginary spectrum in the following we assume that g admits a closed convex inn g invariant cone w g with non empty elliptic interior w 0 if g is a connected lie group with lie algebra g we write s g exp iw for the complex ol shanskii semigroup associated to g and w which may be understood as a quotient by 1 g of the universal covering semigroup of expgc g iw with gc a simply connected complex lie group with lie algebra gc we note that the interior s 0 g exp iw 0 of s carries a complex manifold structure and we write hol s 0 for the frechet space of holomorphic functions on s 0 one of the main topics in the complex analysis on complex ol shanskii semigroups is the study of hilbert spaces of holomorphic functions on s 0 two of them are of particular interest namely the hardy space

tests of a method for estimating corrections to scaling from series the author studies a recently developed pade type method of series analysis which allows for the leading confluent singularity a number of properties are described and by applying the method to various test series some pitfalls of the technique are revealed

position space renormalisation group for isolated polymer chains we develop a cell position space renormalisation group psrg with which we study the scaling properties of isolated polymer chains we model a chain by a self avoiding walk constrained to a lattice for rescaling factors b s 6 we calculate recursion relations analytically on the square lattice with several different choices for the psrg weight function we also calculate implicit cell to cell transformations in which a cell of size b is rescaled to a cell of size b the results of these psrgs improve both as b increases and as b b 1 in addition we construct a true infinitesimal psrg transformation which appears to become exact as the dimensionality d approaches 1 we obtain the closed form expression for the correlation length exponent u d l d in d the flory formula deviates from this already at first order in d 1 we also develop a constant fugacity monte carlo method which enables us to simu late in an unbiased way within the grand canonical ensemble chains of up to lo3 bonds with this method we extend the psrg to larger cells b s 150 on the square lattice our numerical method provides high statistical accuracy for all cell sizes however in the range of b we study the asymptotic behaviour of our results appears to depend on the choice of weight function one weight function provides smooth behaviour as a function of b and with it we extrapolate to find u 0 756 0 004 further work is required to resolve the apparent anomalies in the results based on the other weight functions

non gaussian fixed points of the block spin transformation hierarchical model approximation with the use of analyticity techniques recently developed by the authors the e and 1 n expansion type arguments are turned into a rigorous control of the non gaussian fixed point of the hierarchical model renormalization group the present approach should extend beyond the hierarchical approximation and result in mathematical theory of the critical point of statistical mechanics or quantum field theory in three dimensions for small e or largen

critical exponents hyperscaling and universal amplitude ratios for two and three dimensional self avoiding walks we make a high precision monte carlo study of two and three dimensional self avoiding walks saws of length up to 80 000 steps using the pivot algorithm and the karp luby algorithm we study the critical exponents v and 2 triangle sub 4 gamma as well as several universal amplitude ratios in particular we make an extremely sensitive test of the hyperscaling relation dv 2 triangle sub 4 gamma in two dimensions we confirm the predicted exponent v 3 4 and the hyperscaling relation we estimate the universal ratios 0 14026 0 00007 0 43961 0 00034 and psi 0 66296 0 00043 68 confidence limits in three dimensions we estimate v 0 5877 0 0006 with a correction to scaling exponent triangle sub 1 0 56 0 03 subjective 68 confidence limits this value for v agrees excellently with the field theoretic renormalization group prediction but there is some discrepancy for triangle 1 earlier monte carlo estimates of v which were approximately 0 592 are now seen to be biased by corrections to scaling we estimate the universal ratios 0 1599 0 0002 and psi 0 2471 0 0003 since psi 0 hyperscaling holds the approach to psi is from above contrary to the prediction of the two parameter renormalization group theory we critically reexamine this theory and explain where the error lies in an appendix we prove rigorously modulo some standard scalingmore assumptions the hyperscaling relation dv 2 triangle sub 4 gamma for two dimensional saws less

statistical quality control of variety trial data summary i propose detection criteria for identifying an abnormal or erroneous data vector provided by a single variety trial in a longer series of variety trials the test criteria are based on the linear effects estimated separately for each studied trial using global variance components estimated from the whole series of variety trials the criteria comprise three mutually independent test statistics the first one is a quadratic form in the estimated fixed effects the second one is a quadratic form in the estimated realized linear random effects not including the residual effects and the third one is a quadratic form in the estimated realized residual effects under the null hypothesis defining a valid data vector the three quadratics have independent x2 distributions under natural alternative hypotheses they have noncentral x2 distributions decomposing the total variation of the data vector studied into quadratic forms due to different types of the realized linear effects intuitively justifies the resulting test criteria the decomposition may also be used to show that the resulting tests are likelihood ratio tests i further present computational procedures that allow us to dispense with the need for prior estimation of the linear effects

four dimensional polymer collapse ii interacting self avoiding trails we have simulated four dimensional interacting self avoiding trails isat on the hypercubic lattice with standard interactions at a wide range of temperatures up to length 4096 and at some temperatures up to length 16384 the results con3rm the earlier prediction using data from a non standard model at a single temperature of a collapse phase transition occurring at 3nite temperature moreover they are in accordwith the phenomenological theory originally proposed by lifshitz grosberg andkhokhlov in three d andrecently given new impetus by its use in the description of simulational results for four dimensional interacting self avoiding walks isaw in fact we argue that the available data is consistent with the conclusion that the collapse transitions of isat andisaw lie in the same universality class in contrad iction with long standing predictions we deduce that there exists a pseudo 3rst order transition for isat in four dimensions at 3nite lengths while the thermodynamic limit is described by the standard polymer mean 3eld theory giving a second order transition in contradiction to the prediction that the upper critical dimension for isat is du 4 c 2001 elsevier science b v all rights reserved

polymer conformations through wiggling a new monte carlo method is proposed which allows for the efficient generation of equilibrium conformations of polymer chains in two and three dimensions the method treats each site monomer as a potential pivot around which a new conformation may be generated by rotating a portion of the chain the method does not suffer from the severe attrition associated with the simple sampling of self avoiding walks and may be extended to treat the interacting polymer chain the authors find in two dimensions that nu 0 748 or 0 005 exact 0 750 and in three dimensions nu 0 595 or 0 005 series expansion and renormalisation group predict nu approximately 0 588 the end end distances calculated for shorter chains are in good agreement with the exact values from enumeration techniques

modelling variance heterogeneity residual maximum likelihood and diagnostics the assumption of equal variance in the normal regression model is not always appropriate to attempt to eliminate unequal variance a transformation is often used but if the transformation is not successful or the variances are of intrinsic interest it may be necessary to model the variances in some way we consider the normal regression model when log linear dependence of the variances on explanatory variables is suspected detection of the dependence estimation and tests of homogeneity based on full and residual maximum likelihood are discussed as are regression diagnostic methods based on case deletion and log likelihood displacement

construction of a non trivial planar field theory with ultraviolet stable fixed point we study a 4 4 planar euclidean quantum field theory with propagator 1 p 2 2 0 with the help of the tree expansion of gallavotti and nicolo 1 this non renormalizable theory is shown to have a non trivial ultraviolet stable fixed point at negative coupling constant the vicinity of the fixed point is discussed

on the critical behaviour of self avoiding walks for pt i see ibid vol 22 p 1839 1989 for the self avoiding walk problem the coefficients of the chain generating function and of the generating function for the sum of square end to end distances have been extended to 20 terms for the triangular lattice to 27 terms for the diamond lattice to 21 terms for the simple cubic lattice and to 16 terms for the bcc lattice precise estimates of the critical points are obtained and for the exponents we find that gamma 1 161 or 0 002 and nu 0 592 or 0 003 encompasses all the three dimensional lattice data

mean field critical behaviour for correlation length for percolation in high dimensions extending the method of 27 we prove that the corrlation length of independent bond percolation models exhibits mean field type critical behaviour i e p p c p 1 2 asp p c in two situations i for nearest neighbour independent bond percolation models on ad dimensional hypercubic lattice d withd sufficiently large and ii for a class of spread out independent bond percolation models which are believed to belong to the same universality class as the nearest neighbour model in more than six dimensions the proof is based on and extends a method developed in 27 where it was used to prove the triangle condition and hence mean field behaviour of the critical exponents and 2 for the above two cases

the continuous spin ising model g 0 φ 4 d field theory and the renormalization group we have used the method of high temperature series expansions to investigate the critical point properties of a continuous spin ising model and g0 4 d euclidean field theory we have computed through tenth order the hightemperature series expansions for the magnetization susceptibility second derivative of the susceptibility and the second moment of the spin spin correlation function on eight different lattices our analysis of these series is made using integral and pade approximants in three dimensions we find that hyperscaling fails for sufficiently ising like systems the strong coupling limit of g0 4 3 depends on how the ultraviolet cutoff is removed the level contours of the renormalized coupling constant for this model in theg0 correlation length plane exhibit a saddle point if the ultraviolet cutoff is removed beforeg0 the usual field theory results and the renormalization group fixed point with hyperscaling is obtained if the order of these limits is reversed the ising model limit where hyperscaling fails and the field theory is trivial is obtained in four dimensions we find that hyperscaling fails completely g0 4 4 is trivial for all g0 when the ultraviolet cutoff is removed

non gaussian scaling limits hierarchical model approximation we extend a previous analysis of non gaussian fixed points of the block spin renormalization group in hierarchical models to a long distance analysis of the correlation functions

grand canonical simulations of the interacting self avoiding walk model we report the results obtained from simulations of the interacting self avoiding walk isaw model on the square and simple cubic lattices in particular we verify a new scaling form for the canonical partition function in the low temperature phase as proposed by owczarek et al we also obtain estimates of the critical exponent in two dimensions finally we obtain good agreement with previous studies on the value of a correction to scaling amplitude at the point on the simple cubic lattice which is in disagreement with a field theoretic prediction

a scaling theory of the collapse transition in geometric cluster models of polymers and vesicles much effort has been expended in the past decade to calculate numerically the exponents at the collapse transition point in walk polygon and animal models the crossover exponent phi has been of special interest and sometimes is assumed to obey the relation 2 alpha 1 phi with the alpha the canonical thermodynamic exponent that characterizes the divergence of the specific heat the reasons for the validity of this relation are not widely known the authors present a scaling theory of collapse transitions in such models the free energy and canonical partition functions have finite length scaling forms whilst the grand partition function has a tricritical scaling form the link between the grand and canonical ensembles leads to the above scaling relation they then comment on the validity of current estimates of the crossover exponent for interacting self avoiding walks in two dimensions and propose a test involving the scaling relation which may be used to check these values

smooth finite size behaviour of the three dimensional ising model abstract we have obtained monte carlo results for finite simple cubic ising models at criticality the susceptibility data are consistent with a smooth approach to the asymptotic behaviour for large system sizes

monte carlo simulation of 3d self avoiding walks presents simulation results for 3d self avoiding walks of moderate length n or 2000 using a recently introduced recursive sampling method it is shown that this method is indeed maximally efficient for determining the connectivity constant mu combining the data with previous results from exact enumerations and from simulations of very long walks using the pivot algorithm the author obtains very precise estimates of mu and of the critical exponents gamma and nu he also points out significant deviations from uniformity in a very popular random number generator which was considered safe until now

convergence of self avoiding random walk to brownian motion in high dimensions it is proved that in sufficiently high dimensions the scaled self avoiding random walk on the hypercubic lattice converges in distribution to brownian motion convergence of the finite dimensional distributions was shown elsewhere in this paper tightness is shown

universal distance ratios for two dimensional polymers by using a quantitative version of the c theorem in conformal theories the authors determine some universal geometrical features of two dimensional critical systems with emphasis on the ratios of mean square distances for polymers

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

hyperscaling and universality in 3 dimensions abstract a brief discussion of the relationships between critical exponents known as hyperscaling and the universality of amplitudes at the critical point in 3 dimensions is given numerical evidence for hyperscaling based on series analysis of ising models is reviewed with special emphasis on the assumptions underlying the various methods of analysis revised critical exponent estimates based on a preliminary analysis of recently extended series on the body centered cubic lattice are presented

scaling in the collapsed polymer phase exact results the author derives an exact scaling form for the low temperature partition function in a model of polymer collapse this confirms series work and so gives the exponents sigma 1 2 gamma 1 4 and chi 3 4 exactly the model considered is a variant of the self interacting partially directed self avoiding walk in two dimensions

the diffusion of self avoiding random walk in high dimensions we use the brydges spencer lace expansion to prove that the mean square displacement of at step strictly self avoiding random walk in thed dimensional square lattice is asymptotically of the formdt ast approaches infinity ifd is sufficiently large the diffusion constantd is greater than one

the plancherel theorem for invariant hilbert spaces we calculate explicitly the plancherel measure for certain hilbert spaces of holomorphic functions naturally associated to affine symmetric spaces with holomorphic discrete series

two dimensional polymers universality and correction to scaling improved monte carlo methods have been used to study the asymptotic behaviour of self avoiding walks on two dimensional lattices the mean square end to end distance rn2 and radius of gyration sn2 are both found to scale as n2v with exponent values very close to the expected v 3 4 and an amplitude ratio that is universal small n deviations of rn2 from the asymptotic results indicate a correction to scaling exponent delta 1 a value that differs from previous estimates

exact and monte carlo study of adsorption of a self interacting polymer chain for a family of three dimensional fractals we study the problem of adsorption of self interacting linear polymers situated in fractal containers that belong to the three dimensional 3d sierpinski gasket sg family of fractals each member of the 3d sg fractal family has a fractal impenetrable 2d adsorbing surface which is in fact 2d sg fractal and can be labelled by an integer b 2 b by applying the exact and monte carlo renormalization group mcrg method we calculate the critical exponents associated with the mean squared end to end distance of polymers and associated with the number of adsorbed monomers for a sequence of fractals with 2 b 4 exactly and 2 b 40 monte carlo we find that both and monotonically decrease with increasing b that is with increase of the container fractal dimension df and the interesting fact that both functions b and b cross the estimated euclidean values besides we establish the phase diagrams for fractals with b 3 and b 4 which reveal the existence of six different phases that merge together at a multi critical point whose nature depends on the value of the monomer energy in the layer adjacent to the adsorbing surface

the pivot algorithm a highly efficient monte carlo method for the self avoiding walk the pivot algorithm is a dynamic monte carlo algorithm first invented by lal which generates self avoiding walks saws in a canonical fixed n ensemble with free endpoints heren is the number of steps in the walk we find that the pivot algorithm is extraordinarily efficient one effectively independent sample can be produced in a computer time of ordern this paper is a comprehensive study of the pivot algorithm including a heuristic and numerical analysis of the acceptance fraction and autocorrelation time an exact analysis of the pivot algorithm for ordinary random walk a discussion of data structures and computational complexity a rigorous proof of ergodicity and numerical results on self avoiding walks in two and three dimensions our estimates for critical exponents are 0 7496 0 0007 ind 2 and 0 592 0 003 ind 3 95 confidence limits based on saws of lengths 200 n 10000 and 200 n 3000 respectively

a note on restricted maximum likelihood estimation with an alternative outlier model summary for single outliers in normal theory fixed effects models a mean slippage model is commonly used an alternative is to model the outlier as arising from an unknown observation with inflated variance maximum likelihood estimates for the position of the outlier under the two models need not agree this paper considers maximizing a restricted part of the likelihood to estimate the variance parameters and character izes these estimates in terms of standard least squares parameters it is shown that the residual variance and outlier position are the same under both models in a recent paper cook holschuh and weisberg 1982 consider two models for single outliers in flxed effects linear models one is based on the assumption that contamination gives rise to slippage in the expected values of the observations weisberg 1980 section 5 3 cook et al point out the key role of studentized residuals in this model for instance in estimating the position of an outlier or testing for the presence of an outlier alternatively one can assume that an outlier arises from an error term with an increased variance cook et al argue intuitively that it seems reasonable that studentized residuals might play a similar role under this alternative model but show that maximum likelihood estimates of outlier position can differ under these two models cook et al note that their models can be fitted into a linear model framework discussed by harville 1977 they do not note that harville recommends a restricted maximum likelihood reml approach using only a restricted part of the likelihood to estimate the variance para meters patterson and thompson 1971 noted that this reml approach takes account of loss of degrees of freedom in estimating flxed effects in this note reml estimates for the alternative model are derived and expressed in standard least squares statistics it is shown that the observation having the largest studentized residual is the one picked out as the outlier

new lower bounds on the self avoiding walk connective constant we give an elementary new method for obtaining rigorous lower bounds on the connective constant for self avoiding walks on the hypercubic lattice d the method is based on loop erasure and restoration and does not require exact enumeration data our bounds are best for highd and in fact agree with the first four terms of the 1 d expansion for the connective constant the bounds are the best to date for dimensionsd 3 but do not produce good results in two dimensions ford 3 4 5 and 6 respectively our lower bound is within 2 4 0 43 0 12 and 0 044 of the value estimated by series extrapolation

analytic extension of the holomorphic discrete series introduction the embedding r c naturally divides c into two half planes each with r as boundary these domains together with their function theory play an important role in the harmonic analysis of r as but one example there is the theorem of paley and wiener that describes any square integrable function on r as a sum of boundary values of holomorphic functions in hardy spaces on these domains much of the theory has natural extensions to r to tube domains in c based on cones and even to more general siegel domains however the dominant influence is abelian harmonic analysis on the other hand if g is a semisimple lie group over r it may often be embedded in its natural complexification gc does any of the abelian

on the corrections to scaling in three dimensional ising models the leading correction to scaling amplitudes for the spin 1 2 nearest neighbor sc bcc and fee ising models are considered with the particular aim of determining their signs on the basis of previous two variable series analyses by chen fisher and nickel and renormalization group 4 d expansions it is concluded that the correction amplitudes for the susceptibility correlation length specific heat and spontaneous magnetization arenegative for all three lattices thus for example the effective exponent eff t asymptotically approaches the true susceptibility exponent fromabove other earlier and more recent high temperature series and field theoretic analyses are seen to be consistent with this result however the usual nonasymptotic perturbative field theoretic approaches are essentially committed to positive correction amplitudes the question of the signs therefore relates directly to the applicability of these non asymptotic field theoretic calculations to three dimensional ising models as well as to different experimental systems

mean field critical behaviour for percolation in high dimensions the triangle condition for percolation states that sum limits x y tau 0 x tau 0 y cdot tau y 0 is finite at the critical point where x y is the probability that the sitesx andy are connected we use an expansion related to the lace expansion for a self avoiding walk to prove that the triangle condition is satisfied in two situations i for nearest neighbour independent bond percolation on thed dimensional hypercubic lattice ifd is sufficiently large and ii in more than six dimensions for a class of spread out models of independent bond percolation which are believed to be in the same universality class as the nearest neighbour model the class of models in ii includes the case where the bond occupation probability is constant for bonds of length less than some large number and is zero otherwise in the course of the proof an infrared bound is obtained the triangle condition is known to imply that various critical exponents take their mean field bethe lattice values gamma beta 1 delta delta t 2 t underset raise0 3em hbox smash scriptscriptstyle geqslant 2 and that the percolation density is continuous at the critical point we also prove thatv2 in i and ii wherev2 is the critical exponent for the correlation length

self avoiding walk in five or more dimensions i the critical behaviour we use the lace expansion to study the standard self avoiding walk in thed dimensional hypercubic lattice ford 5 we prove that the numbercn ofn step self avoiding walks satisfiescn a n where is the connective constant i e 1 and that the mean square displacement is asymptotically linear in the number of steps i e v 1 2 a bound is obtained forcn x the number ofn step self avoiding walks ending atx the correlation length is shown to diverge asymptotically like z 1 2 the critical two point function is shown to decay at least as fast as x 2 and its fourier transform is shown to be asymptotic to a multiple ofk 2 ask 0 i e 0 we also prove that the scaling limit is gaussian in the sense of convergence in distribution to brownian motion the infinite self avoiding walk is constructed in this paper we prove these results assuming convergence of the lace expansion the convergence of the lace expansion is proved in a companion paper

sign of corrections to scaling amplitudes field theoretic considerations and results for self repelling walks i discuss the application of renormalized field theory to such critical systems where the renormalized coupling approaches the fixed point from the wrong strong coupling side in contrast to a belief sometimes expressed in the literature i find that also this situation can be described within the standard formalism only the interpretation of the strong coupling branch relies on the existence of a finite cutoff i illustrate these considerations with an analysis of monte carlo data for self avoiding walks finding that the data support the theory in all respects however it is stressed that the nonuniversal parameters of the renormalized theory in general have no simple relation to the parameters of the underlying bare model