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On a lighter note, here is a very interesting blog piece, bringing some sort of similarity to the giant component behaviour on a pile of staple pins. This is sort of a layman view of the Erdos Renyi explanation.
In one version of the Erdős-Rényi process, one start with a set of isolated vertices and then keep adding random edges one at a time; More specifically, at each stage one choose two vertices at random from among all pairs that are not already connected, then draw an edge between them. It turns out there’s a dramatic change in the nature of the graph when the number of edges reaches . Below this threshold, the graph consists of many small, isolated components; above , the fragments coalesce into one giant component that includes almost all the vertices. “The Birth of the Giant Component” was later described in greater detail in an even bigger paper–it filled an entire issue of Random Structures and Algorithms (1993, 4:233–358)–by Svante Janson, Donald E. Knuth, Tomasz Luczak and Boris Pittel.
Ofcourse Joel Spencer has written a beautiful article on AMS commemurating the golden anniversity of the giant component.
I am very thrilled to learn that Ruediger Urbanke has won the 2011 (Koji) Kobayashi award. He and Tom Richardson are named the 2010 receipients of the famous Kobayashi award. Rudi and Tom are awarded Kobayashi prize “for developing the theory and practice of transmitting data reliably at rates approaching channel capacity.” They truly deserve this. Looking at the list of earlier Kobayashi award winners, it really is a place of pantheon of greats. Gottfried Ungerboeck, Don Coppersmith, Rivest, Shamir, Addleman, Jack Wolf, Berlekamp and so on are among the famous awardees of the past.
When pointed this to Rudi, he was as usual every modest about these. I am sure I will get to have a coffee treat from him, in Lausanne! Place Palud or Ouchy?