- The Giant Component: The Golden Anniversary Joel Spencer
- Explosive Percolation in Random Networks
- P. Erdos and L. Lov asz 1975, Problems and results on 3-chromatic hypergraphs and some related questions, in: In nite and Finite Sets A. Hajnal et al., eds., North-Holland, Ams-
- to the entire argument.) Given that the probes find E 1 ; . . . ; E k their birth times t E 1
- V63.0344 Undergraduate Algebra II, Spring 11 Time Monday, Wednesday 11:0012:15
- Suppose p ? \Lambda p k\Gamma1;s , all s. Fix an arbitrary tree T with any k \Gamma1 specified vertices v 1 ; . . . ; v k\Gamma1 and with any specified integers d 1 ; . . . ; d k\Gamma1 with each
- [2] P. Erdos, Problems and results in additive number theory, in Colloque sur la Th'eorie des Nombres (CBRM), Bruxelles, 1955, 127137.
- Fundamental Algorithms, Assignment 4 1. Consider the recursion T(n) = 9T(n/3) + n2 with initial value T(1) =
- Fundamental Algorithms, Problem Set 2 Due Tuesday, September 21
- Fundamental Algorithms, Problem Set 1 Solutions 1. Let A is a max-heap with heapsize fifty million, being used as a priority
- Fundamental Algorithms, Problem Set 3 1. Write each of the following functions as (g(n)) where g(n) is one of
- Fundamental Algorithms, Problem Set 2 Due Tuesday, September 21
- Fundamental Algorithms, Assignment 4 1. Consider the recursion T (n) = 9T (n/3) +n 2 with initial value T (1) =
- Fundamental Algorithms, Problem Set 1 Solutions 1. Let A is a maxheap with heapsize fifty million, being used as a priority
- Fundamental Algorithms, Problem Set 3 1. Write each of the following functions as #(g(n)) where g(n) is one of
- Joel Spencer Some of our best work never appears in journal form. It is in notes sent
- [1] N. Alon and J. Spencer, The Probabilistic Method, 2nd ed., John Wiley, 2000. [2] E.R. Berlekamp, Block coding for the binary symmetric channel with noiseless, de
- of its children the ith and (i + 1)st coordinates are at least :48x \Lambda by induction, also large. 2
- 7 B. Bollob as.The chromaticnumberof randomgraphs. Combinatorica 8:49-55, 8 P. Erdos. Some remarks on the theory of graphs. Bulletin of the Amer. Math.
- [1] N. Alon, J. Spencer, The Probabilistic Method, John Wiley, New York, [2] J. Beck, On 3chromatic hypergraphs, Discrete Math 24 (1978), pp 127
- Algebra V63.0344 Assignment 6
- Throughout these notes we will be considering polynomials over Z 2 , that is, f(x) # Z 2 [x]. The methods discussed readily extend to Z p [x].
- Simulating a Random Walk with Constant Error 9 3. Acknowledgements
- 1 The Erdos-Renyi Phase Transition In their great 1960 work On the Evolution of Random Graphs, Paul Erdos
- The Elementary Proof of the Prime
- Robin Moser makes Lovasz Local Lemma Algorithmic! Notes of Joel Spencer
- Counting Connected Graphs Asymptotically Remco van der Hofstad
- Birth Control for Giants Joel Spencer
- c 2008 by Institut Mittag-Leffler. All rights reserved Ark. Mat., 00 (2008), 124
- THE SECOND LARGEST COMPONENT IN THE SUPERCRITICAL 2D HAMMING GRAPH
- Random subgraphs of finite graphs: III. The phase transition for the n-cube
- SUDDEN EMERGENCE OF A GIANT k-CORE IN A RANDOM GRAPH.
- THE COMPLEXITY OF RANDOM ORDERED JOEL H. SPENCER AND KATHERINE ST. JOHN
- [1] N. Alon and J. Spencer, The Probabilistic Method, 2nd ed., John Wiley, 2000. [2] E.R. Berlekamp, Block coding for the binary symmetric channel with noiseless, de-
- The Two-Batch Liar Game over an Arbitrary Channel Ioana Dumitriu
- 2 P. Erdos, Problems and results in additive number theory, in Colloque sur la Th eorie des Nombres CBRM, Bruxelles, 1955, 127-137.
- The function ACKP is called the Ackermann function. There are sev-eral similar formulations. The extreme growth rate of ACKP is illustrated
- 12 J.E. Graver, J. Yackel, Some graph theoretic results associated with Ramsey's theorem. J. Combinatorial Theory 4 1968, 125-175
- The class of 1 r is z and z 2 Rx. The class z0 of 0 Lz and Rx. As z 2 Lz Rx, z = z0. Thus 1;ir under M and 1;i0
- 1 Erdos on x+y=n 2 Erdos-Hanani
- game and its reversal tend to be quite similar. The reversal of the Liar Game is particularly intriguing. Lets call it the
- Counting Connected Graphs Asymptotically Remco van der Hofstad #
- A Scaling Result for Explosive Processes M. Mitzenmacher
- [12] J.E. Graver, J. Yackel, Some graph theoretic results associated with Ramsey's theorem. J. Combinatorial Theory 4 (1968), 125175
- P. Erdos and L. Lov'asz (1975), Problems and results on 3chromatic hypergraphs and some related questions, in: Infinite and Finite Sets (A. Hajnal et al., eds.), NorthHolland, Ams
- and so 24 becomes \Gamma ln Pr[A \Lambda
- A POINT PROCESS DESCRIBING THE COMPONENT SIZES IN THE CRITICAL WINDOW OF THE RANDOM GRAPH
- The Liar Game over an Arbitrary Channel Ioana Dumitriu
- and so 24 becomes t+dt ,lnPr A
- Random subgraphs of finite graphs: II. The lace expansion and the triangle condition
- Algebra V63.0344 Assignment 1
- Algebra V63.0344 Assignment 8 Solutions
- GALOIS THEORY NOTES Prof. J. Spencer
- of its children the i-th and i + 1-st coordinates are at least :48x by induction, also large. 2
- [1] Ed Bender, E. Rodney Can eld and B.D. McKay, The Asymptotic Number of Labeled Connected Graphs with a Given Number of Vertices and Edges,
- Algebra V63.0344 Assignment 12 Solutions
- Magic Squares Let F be a finite field with at least three elements. We create Latin
- Deterministic Random Walks on the Integers # Joshua Cooper + Benjamin Doerr # Joel Spencer
- A POINT PROCESS DESCRIBING THE COMPONENT SIZES IN THE CRITICAL WINDOW OF THE RANDOM GRAPH
- [18] J. Lynch, Almost Sure Theories, Ann. Math. Logic 18 (1980), 91135 [19] J. Lynch, Properties of Sentences about Very Sparse Random Graphs,
- Birth Control for Giants Joel Spencer
- Algebra V63.0344 Assignment 11 Solutions
- 1 The Rich Get Richer Consider two bins, each of which initially have one ball. At each time
- Nearly perfect matchings in regular simple hypergraphs Noga Alon # JeongHan Kim + Joel Spencer #
- [22] R. Lipton and R. Tarjan: A separator theorem for planar graphs, SIAM J. Applied Mathe-matics 36 (1979), 177{189.
- his being, showed us the Temple of Mathematics. The Pages of the Book were there, we had only to open them. Did there, for every k;r 0, exist
- Joel H. Spencer Professor of Mathematics and Computer Science
- Joel H. Spencer Professor of Mathematics and Computer Science
- [7] B. Bollob'as. The chromatic number of random graphs. Combinatorica 8:4955, [8] P. Erdos. Some remarks on the theory of graphs. Bulletin of the Amer. Math.
- his being, showed us the Temple of Mathematics. The Pages of the Book were there, we had only to open them. Did there, for every k; r ? 0, exist
- Algebra V63.0344 Assignment 7 Solutions
- "imvol2" --2005/8/8 --14:01 --page 153 --#1 Internet Mathematics Vol. 2, No. 2: ??-??
- Deterministic Random Walks on the Integers Joshua Cooper
- 18 J. Lynch, Almost Sure Theories, Ann. Math. Logic 18 1980, 91-135 19 J. Lynch, Properties of Sentences about Very Sparse Random Graphs,
- to the entire argument. Given that the probes nd E1;...;Ek their birth-times tE1;...;tEk are uniform in 0;t , just as with the birth model. As
- [12] Propp, J. and Wilson, D. Exact sampling with coupled Markov chains and appli-cations to statistical mechanics. Random Structures and Algorithms 9:223{252,
- [1] Erdos on x+y=n [2] ErdosHanani
- c ,2p G = O 1 ,2p ln + ln ,1
- Complexity and Effective Prediction Abraham Neyman
- Robin Moser makes Lovasz Local Lemma Algorithmic! Notes of Joel Spencer
- Simulating a Random Walk with Constant Error 9 3. Acknowledgements
- The Giant Component: The Golden Anniversary Joel Spencer
- Logic and Random Structures Joel Spencer
- [9] J. Spencer, Ten Lectures on the Probabilistic Method, SIAM, Philadelphia, 1987. [10] S. K. Stein, Transversals of Latin squares and their generalizations, Pacific J. Math. 59,
- Joel H. Spencer Professor of Mathematics and Computer Science
- 9 J. Spencer, Ten Lectures on the Probabilistic Method, SIAM, Philadelphia, 1987. 10 S. K. Stein, Transversals of Latin squares and their generalizations, Paci c J. Math. 59,
- Algebra V63.0344 Assignment 9 Solutions
- Algebra V63.0344 Assignment 3
- The TwoBatch Liar Game over an Arbitrary Channel Ioana Dumitriu #
- Joel H. Spencer Professor of Mathematics and Computer Science
- The class of fi 1 \Delta \Delta \Delta fi r is z and z 2 R x . The class z 0 of fi 0 1 \Delta \Delta \Delta fi 0
- game and its reversal tend to be quite similar. The reversal of the Liar Game is particularly intriguing. Lets call it the
- Rough Notes on Bansal's Algorithm Joel Spencer
- The function ACKP is called the Ackermann function. (There are sev eral similar formulations.) The extreme growth rate of ACKP is illustrated
- A Scaling Result for Explosive Processes M. Mitzenmacher # R. Oliveira + J. Spencer #
- 1; . . . ; k being the special vertices and let G \Lambda (n; p) be G(n; p) conditioned on this copy. As before we let Pw (a; b) be the expected number of paths of
- Algebra V63.0344 Assignment 2
- Algebra V63.0344 Assignment 10 Solutions
- Joel Spencer Some of our best work never appears in journal form. It is in notes sent
- 1;...;k being the special vertices and let Gn;p be Gn;p conditioned on this copy. As before we let Pwa;b be the expected number of paths of
- Logic and Random Structures Joel Spencer
- 1 N. Alon, J. Spencer, The Probabilistic Method, John Wiley, New York, 2 J. Beck, On 3-chromatic hypergraphs, Discrete Math 24 1978, pp 127-
- Random subgraphs of finite graphs: I. The scaling window under the triangle condition
- [6] B. Bollob as and O.M. Riordan, The diameter of a scale-free random graph, submitted for publication.
- ae 1=5 !1 c \Gamma2 p
- Nearly perfect matchings in regular simple hypergraphs Jeong-Han Kim
- Suppose p pk,1;s, all s. Fix an arbitrary tree T with any k,1 speci ed vertices v1;...;vk,1 and with any speci ed integers d1;...;dk,1 with each
- V63.0344 Undergraduate Algebra II, Spring 12 Time Monday, Wednesday 11:00-12:15
- Algebra V63.0344 Assignment 3
- Random Graphs Assignment 1. Solutions
- Algebra V63.0344 Assignment 2
- Random Graphs Assignment 6 Solutions 1. Here is a problem from work done by Roberto Oliveira, who received
- Algebra V63.0344 Assignment 5 Solutions
- Random Graphs Assignment 3. Solutions
- Magic Squares Let F be a finite field with at least three elements. We create Latin
- Random Graphs Assignment 2. Solutions
- Random Graphs Assignment 5. SOLUTIONS
- Algebra V63.0344 Assignment 1
- Algebra V63.0344 Assignment 6 Solutions
- Random Graphs Assignment 4. Solutions
- Random Graphs --Prof. Spencer Note on n choose k asymptotcs
- V63.0344 Undergraduate Algebra II, Spring 12 Time Monday, Wednesday 11:0012:15
- Magic Squares Let F be a finite field with at least three elements. We create Latin
- Random Graphs Assignment 1. Solutions
- Algebra V63.0344 Assignment 1
- Algebra V63.0344 Assignment 6 Solutions
- Random Graphs Prof. Spencer Note on n choose k asymptotcs
- Random Graphs Assignment 2. Solutions
- Random Graphs Assignment 4. Solutions
- Algebra V63.0344 Assignment 5 Solutions
- Algebra V63.0344 Assignment 2
- Scribe: Yitao Li Date: 02/13/2012
- Random Graphs Assignment 6 Solutions 1. Here is a problem from work done by Roberto Oliveira, who received
- Random Graphs Assignment 5. SOLUTIONS
- Algebra V63.0344 Assignment 3
- Random Graphs Assignment 3. Solutions
- V63.0344 Undergraduate Algebra II Notes: Spring 2012 Professor Joel Spencer, Prepared by Frank Hsu